Monochromatic Color

In this paper, we utilize the Ramsey theory to investigate the geometrical characteristics of closed contours. We begin by examining a set of six points arranged on a closed contour and connected as a complete graph. We assign the downward-pointing edges a red color, while coloring the remaining edges green. Our analysis establishes that the curve must contain at least one monochromatic triangle. This finding has practical applications in the study of dynamical billiards. Our second result is derived from the Jordan curve theorem and the Ramsey theorem. Finally, we discuss Ramsey constructions arising from differential geometry. Applications of the Ramsey theory are discussed.

The profile of suspended silicon nitride thin films patterned with one-dimensional subwavelength grating structures is investigated using Atomic Force Microscopy. We first show that the results of the profilometry can be used as input to Rigorous Coupled Wave Analysis simulations to predict the transmission spectrum of the gratings under illumination by monochromatic light at normal incidence and compare the results of the simulations with experiments. Secondly, we observe sharp vertical deflections of the films at the boundaries of the patterned area due to local modifications of the tensile stress during the patterning process. These deflections are experimentally observed for various grating structures and investigated on the basis of a simple analytical model as well as finite element method simulations.

An infinite graph is highly connected if the complement of any subgraph of smaller size is connected. We consider weaker versions of Ramsey's Theorem asserting that in any coloring of the edges of a complete graph there exist large highly connected subgraphs all of whose edges are colored by the same color.

Exposure of the retina of the rhesus monkey to visible and infrared radiation from CW optical sources like the Sun, xenon lamps, etc. produces small lesions or scotomata which may be classified as thermal or photochemical, depending on the wavelength and duration of exposure. The action spectrum for the production of retinal lesions has been determined for eight monochromatic laser wavelengths extending from 1064 to 441 nm. The corneal power required to produce a lesion decreases by three orders of magnitude in going from 1064 to 441 nm. Exposure to 1064 nm radiation for 1000 s produces a typical thermal lesion at elevated retinal temperatures, whereas a 1000 s exposure to 441 nm light produces a photochemical lesion at power levels too low to raise the retinal temperature by an appreciable amount ( < O.l°C). The two types of lesion have entirely different characteristics as will be discussed in some detail. The photopathology of the photochemical lesion has been studied at postexposure times ranging from 1 h to 90 days and will be demonstrated in a number of histological slides. Moreover, this photopathology correlates well with monocular visual acuity tests in the rhesus monkey as defined by the Landolt ring technique. To further elucidate the differential effects on the retina of short vs long wavelength CW radiation, we have divided a simulated solar spectrum at sea level into two spectral bands, 400--800 nm and 700-1400 nm, and determined the radiant• exposures required to produce very mild lesions on the rhesus retina for exposure times of 1, 10, 100 and 1000 s. To correlate our data with solar retinitis and eclipse blindness the image diameter or spot size on the retina was 159 11m, corresponding to the image size of the Sun on the human retina. Exposure to the 400--800 nm spectrum for durations of 10 s or greater required approximately 400 J/cm 2 to produce a mild photochemical lesion. Reciprocity is maintained over the exposure range 10--1000 s . . Radiant exposure to the 700-1400 nm spectrum, on the other hand, required roughly 69,100 J/cm 2 for a 1000 s exposure. This was a mild thermal lesion. We were unable to produce .a lesion for exposure times less than 1000 s. We interpret these data to mean that solar retinitis and eclipse blindness are primarily photochemical events produced by the short wavelength component of the solar spectrum, and that the infrared component of the solar spectrum plays only a minor role in these retinal pathologies.

Barber&#39;s palmoplantar pustulosis (PPP) is a form of localised pustular psoriasis, affecting the palmar and plantar surfaces. It is a chronic disease, with a deep impact on the patients&#39; quality of life. The Authors discuss a case of Baber Psoriasis successfully treated with monochromatic excimer light.

This study was performed to investigate the accuracies of the synthesized monochromatic images and effective atomic number maps obtained with the new GE Discovery CT750 HD CT scanner. Methods: A Gammex-RMI model 467 tissue characterization phantom and the CT number linearity section of a Phantom Laboratory Catphan 600 phantom were scanned using the dual energy ͑DE͒ feature on the GE CT750 HD scanner. Synthesized monochromatic images at various energies between 40 and 120 keV and effective atomic number ͑Z eff ͒ maps were generated. Regions of interest were placed within these images/maps to measure the average monochromatic CT numbers and average Z eff of the materials within these phantoms. The true Z eff values were either supplied by the phantom manufacturer or computed using Mayneord's equation. The linear attenuation coefficients for the true CT numbers were computed using the NIST XCOM program with the input of manufacturer supplied elemental compositions and densities. The effects of small variations in the assumed true densities of the materials were also investigated. Finally, the effect of body size on the accuracies of the synthesized monochromatic CT numbers was investigated using a custom lumbar section phantom with and without an external fat-mimicking ring. Results: Other than the Z eff of the simulated lung inserts in the tissue characterization phantom, which could not be measured by DECT, the Z eff values of all of the other materials in the tissue characterization and Catphan phantoms were accurate to 15%. The accuracies of the synthesized monochromatic CT numbers of the materials in both phantoms varied with energy and material. For the 40-120 keV range, RMS errors between the measured and true CT numbers in the Catphan are 8-25 HU when the true CT numbers were computed using the nominal plastic densities. These RMS errors improve to 3-12 HU for assumed true densities within the nominal density Ϯ0.02 g / cc range. The RMS errors between the measured and true CT numbers of the tissue mimicking materials in the tissue characterization phantom over the 40-120 keV range varied from about 6 HU-248 HU and did not improve as dramatically with small changes in assumed true density. Conclusions: Initial tests indicate that the Z eff values computed with DECT on this scanner are reasonably accurate; however, the synthesized monochromatic CT numbers can be very inaccurate, especially for dense tissue mimicking materials at low energies. Furthermore, the synthesized monochromatic CT numbers of materials still depend on the amount of the surrounding tissues especially at low keV, demonstrating that the numbers are not truly monochromatic. Further research is needed to develop DE methods that produce more accurate synthesized monochromatic CT numbers.

Purpose:This study was performed to investigate the accuracies of the synthesized monochromatic images and effective atomic number maps obtained with the new GE Discovery CT750 HD CT scanner.Methods:A Gammex‐RMI model 467 tissue characterization phantom and the CT number linearity section of a Phantom Laboratory Catphan 600 phantom were scanned using the dual energy (DE) feature on the GE CT750 HD scanner. Synthesized monochromatic images at various energies between 40 and 120 keV and effective atomic number maps were generated. Regions of interest were placed within these images/maps to measure the average monochromatic CT numbers and average of the materials within these phantoms. The true values were either supplied by the phantom manufacturer or computed using Mayneord&#39;s equation. The linear attenuation coefficients for the true CT numbers were computed using the NIST XCOM program with the input of manufacturer supplied elemental compositions and densities. The effects of sm...

An integral shutter is a device that integrates a white-beam stop, monochromatic-beam (mono-beam) shutters, a safety stop, and a collimator into one assembly to save space in the photon beamline. Various integral shutters have been developed as standard components for the beamlines at the advanced photon source. The integral shutters are designed to be operated in white-beam mode or mono-beam mode. With regard to safety, each mode of operation is secured by locking certain devices in their up or down positions. Some of the components of the integral shutters share designs similar to the front-end shutters or fixed masks. Design details of the integral shutters are presented.

Lyot depolarizers are optical devices made of birefringent materials used for producing unpolarized beams from totally polarized incident light. The depolarization is produced for polychromatic input beams due to the different phase introduced by the Lyot depolarizer for each wavelength. The effect of this device on other types of incident fields is investigated. In particular two cases are analyzed: (i) monochromatic and nonuniformly polarized incident beams and (ii) incident light synthesized by superposition of two monochromatic orthogonally polarized beams with different wavelengths. In the last case, it is theoretically and experimentally shown that the Lyot depolarizer increases the degree of polarization instead of depolarizes.

Non-linear wave-driven processes in plasmas are normally described by either a monochromatic pump wave that couples to other monochromatic waves, or as a random phase wave coupling to other random phase waves. An alternative approach involves an incoherent, random or broadband pump coupling to monochromatic and/or coherent structures in the plasma. This approach can be implemented through the wave kinetic model. In this model, the incoming pump wave is described by either a bunch (for coherent waves) or a sea (for random phase waves) of quasiparticles. A particle-in-cell type code has been developed to perform numerical simulations of such interactions using the quasi-particle approach. This code allows for a comparatively easy description of both random phase and coherent pump pulses coupling to slow electrostatic plasma waves, while providing an extended range of powerful diagnostics leading to a deeper physical insight into the dynamics of the fast waves. As an example, the propagation of short, intense laser pulses through a plasma has been simulated. A sample of the phenomena that can be studied for this case includes modulational instabilities, photon wave breaking and turbulence, and pulse compression, stretching, and chirping. The extensibility of the numerical implementation to other types of fast wave-slow wave interactions is also discussed.

Süper iletken kütle MgB2-xSiCx (% 5) kütle soğurma katsayıları (% 5) 14,16 -36,37 keV enerji aralığında ölçülerek hesaplanmış ve etkili atom sayıları tahmin edilmiştir. Belirlenen enerjileri, 241-Am'in gama ışını fotonları ile ışınlanmış sekonder hedefler kullanılarak elde edildi. X ışınları 5.9 keV'de 150 eV çözünürlüğe sahip Canberra Ultra-LEGe dedektörü kullanılarak sayıldı. Sonuçlar teorik olarak hesaplanan değerlerle karşılaştırıldı ve ortalama bir deneysel hata ile uyumlu olduğu tespit edildi.

A soft X-ray beam-position monitor based on a thin CVD diamond photodetector has been developed for use on third-generation synchrotron radiation facilities, and has been tested on beamlines ID26 and ID12 at the European Synchrotron Radiation Facility. Since diamond exhibits a low absorption to low-energy X-ray photons, this device allows beam-position monitoring with very little beam attenuation at photon energies as low as 2 keV. The devices presented here ®nd their use essentially on low-energy monochromatic beamlines with narrow beam sizes (typically below 1 mm 2 ). Measurements performed on a 20 mm-thick device show that a position sensitivity of 2 mm can readily be achieved with a photon ¯ux attenuation of 22% at 4 keV. This allows permanent in-situ monitoring of beam instabilities during experiments.

Orthosiphon aristatus (O. aristatus) has been used as a popular traditional folk medicine for the treatment of kidney disease. Recent studies have shown that O. aristatus root contains more flavonoids and has higher antioxidant capacity compared to its medicinal parts. However, there is limited knowledge on the mechanisms behind the synthetic biology of flavonoid in all tissues of O. aristatus. Here, we performed high-performance liquid chromatography (HPLC) analysis and comparative transcriptome analyses of flavonoids in all tissues. The content of 4 major flavonoids is significantly higher in roots and leaves compared to stems in O. aristatus. Out of a total of 138,294 Unigenes, the KEGG pathway analysis identified 66 Unigenes encoding 8 key metabolic enzymes involved in the biosynthetic pathway of flavonoid compounds. Additionally, 5,154 on average DEGs involved in flavonoid biosynthesis could be categorised into 58 transcription factor (TF) families. Among the identified DEGs, a total of 5,897 were common to all tissues, with 212 DEGs strongly associated with flavonoid accumulation in root. Several of these key enzyme genes were further validated by quantitative real-time polymerase chain reaction (qRT-PCR). Our research provides novel insights into flavonoids synthetic biology, and highlights O. aristatus root may serve as a valuable resource for medicinal use.

This paper proposes a criterion for locating obstacles by time reversal (TR) of electromagnetic (EM) waves based on the analysis of the density of EM energy map in time domain. Contrarily to a monochromatic study of the TR, the wide-band approach requires to determine the instant of the wave focus. This enables us to locate the focal spots that are indicative of the positions. The criterion proposed is compared to the inverse of the minimum entropy criterion as used in the literature [X. Xu, E.L. Miller, C.M. Rappaport, IEEE Trans. Geosci. Remote Sens. 41, 1804]. An application for the localization of 3D metal targets is proposed using finite integration technique (FIT) as computational tool at the modeling stage. An experimental validation is presented for canonical three-dimensional configurations with two kinds of metal objects.

The ELI-NP facility, currently being built in Bucharest, Romania, will deliver an intense and almost monochromatic gamma beam with tunable energy between 0.2 and 20 MeV. The challenging energy bandwidth of [Formula: see text]0.5% will be adjusted through the collimation system, while the main beam parameters will be measured through a devoted gamma-beam characterization system.[Formula: see text] The gamma-beam characterization system, designed by the EuroGammaS collaboration, consists of four elements: a Compton spectrometer that measures the gamma energy spectrum; a sampling calorimeter for a fast combined measurement of the beam average energy and its intensity, which will be used also as a monitor during machine commissioning and development; a nuclear resonant scattering system for absolute energy inter-calibration of the other detectors; and a gamma beam profile imager to be used for alignment and diagnostics purposes. The collimation and characterization system will be presen...

The Gamma Beam System of ELI-Nuclear Physics is a high brilliance monochromatic gamma source based on the inverse Compton interaction between an intense high power laser and a bright electron beam with tunable energy. The source, currently being assembled in Magurele (Romania), is designed to provide a beam with tunable average energy ranging from 0.2 to 19.5 MeV, rms energy bandwidth down to 0.5% and flux of about 10 8 photons/s. The system includes a set of detectors for the diagnostic and complete characterization of the gamma beam. To evaluate the spatial distribution of the beam a gamma beam profile imager is required. For this purpose, a detector based on a scintillator target coupled to a CCD camera was designed and a prototype was tested at INFN-Ferrara laboratories. A set of analytical calculations and Monte Carlo simulations were carried out to optimize the imager design and evaluate the performance expected with ELI-NP gamma beam. In this work the design of the imager is described in detail, as well as the simulation tools used and the results obtained. The simulation parameters were tuned and cross-checked with the experimental measurements carried out on the assembled prototype using the beam from an x-ray tube.

The graph theory-based approach to the three-body problem is introduced. Vectors of linear and angular momenta of the particles form the vertices of the graph. Scalar products of the vectors of the linear and angular momenta define the colors of the links connecting the vertices. The bi-colored, complete graph emerges. This graph is called the "momenta graph". According to the Ramsey theorem, this graph contains at least one mono-chromatic triangle. This is true even for chaotic motion of three bodies; thus, illustrating the idea supplied by the Ramsey theory, total chaos is impossible. Coloring of the graph is independent on the rotation of frames; however, it is sensitive to Galilean transformations. The coloring of the momenta graph remains the same for general linear transformations of vectors with a positive-definite matrix. For a given motion, changing the order of the vertices does not change the number and distribution of monochromatic triangles. Symmetry of the momenta graph is addressed. The symmetry group remains the same for general linear transformation of vectors of the linear and angular momenta with a positive-definite matrix. Conditions defining conservation of the coloring of the momenta graph are addressed. The notion of the stereographic momenta graph is introduced. Shannon entropy of the momenta graph is calculated. The particular configurations of bodies are addressed, including the Lagrange configuration and the figure eight-shaped motion. The suggested approach is generalized for the quantum field theory with the Pauli-Lubanski pseudo-vector. The suggested coloring procedure is the Lorenz invariant.

In this work, image quality and optical coherence tomography were studied. The results of the study show that there is a very significant difference between ultrasound and optical coherence tomography to produce an image with a different wave. To understand this, we studied the basic principle of optical coherence tomography in the Michelson interferometer using monochromatic and broadband sources. Time-domain and spectral-domain measurements, which exist at the detector level, are briefly described using a glass sample. The time-domain signal strength of the Michelson interferometer using a broadband source is a Gaussian envelope.

Parabolic compound refractive lenses (PCRLs) are high quality hard x-ray imaging optics that can be used to image a synchrotron source onto a sample in a strongly demagnifying setup. This allows to produce an intensive microbeam with lateral extensions in the (sub-)micrometer range. Aluminium PCRLs can be operated in an energy range from about 10keV to 60keV and withstand the high heat load of the white beam of an ESRF undulator source. The microbeam properties using monochromatic and single undulator harmonic ("pink") radiation are discussed, focusing on beam size, depth of field, background, flux, and gain. The large depth of focus allows to scan fairly large samples (a few millimeters in thickness) with a beam of constant lateral extension. This makes tomographic scanning techniques, such as fluorescence microtomography possible. As applications, fluorescence microtomography of plant samples with sub-cellular resolution and the mapping of trace elements in single cancer cells is shown.

Nuclear Resonance Fluorescence (NRF) measurement is a powerful tool for isotope detection for the homeland security such as a non-destructive material testing for identification of special nuclear materials (SNM) hidden in containers at airports or harbours. In this paper, we will discuss on basic design of a hybrid SNM inspection system using a D-D neutron source, detectors of neutron and gamma ray, a quasi-monochromatic gamma ray generator based on the backward Compton scattering of laser light on high-energy electrons, and an NRF gamma ray detection system using a high-speed scintillation detector.

Following a recent article by one of the authors where the concept of complex intensity has been fully developed from the physical point of view and its spectral properties have been highlighted, the present paper focuses on the relationship between sound energy indicators and wave impedance. It will be shown how the specific impedance of monochromatic, plane quasi-stationary and spherical-divergent waves, are related to the complex sound intensity as defined in ["On the physical meaning of the power factor in acoustics", J. Acoust. Soc. Am. 131(1), 269-280 (2012)], suitably normalized to the kinetic energy density. The relationship will be graphically demonstrated to be true along the direction of the active intensity also for 2-D fields with non-vanishing curl.

In this paper, we consider an extension of cycle-complete graph Ramsey numbers to Berge cycles in hypergraphs: for k ≥ 2, a non-trivial Berge k-cycle is a family of sets e 1 , e 2 , . . . , e k such that e 1 ∩e 2 , e 2 ∩e 3 , . . . , e k ∩e 1 has a system of distinct representatives and e 1 ∩ e 2 ∩ • • • ∩ e k = ∅. In the case that all the sets e i have size three, let B k denotes the family of all non-trivial Berge k-cycles. The Ramsey numbers R(t, B k ) denote the minimum n such that every n-vertex 3-uniform hypergraph contains either a non-trivial Berge k-cycle or an independent set of size t. We prove and moreover, we show that if a conjecture of Erdős and Simonovits on girth in graphs is true, then this is tight up to a factor t o(1) as t → ∞.

It has been reported that the 厂批 te of the crossover effcct is af 弖 ' ectcd by the screen light spcctrum ， but the crossover Offect on each wavelength has not been clarified ． We obtained the spectra of the cross 〔⊃ ver effect on ortho and regular xray filmby exposing the film with monochromatic light from a monochrometer ． The spectra had peaks at 500 nm and 450 nm I ' er the regular and ortho films ， respoctively ， and the crossover spectra of the crossovcr effect appears

Ramsey's Theorem guarantees for every graph H that any 2-edge-coloring of a sufficiently large complete graph contains a monochromatic copy of H. In 1962, Erdős conjectured that the random 2-edge-coloring minimizes the number of monochromatic copies of K k , and the conjecture was extended by Burr and Rosta to all graphs. In the late 1980s, the conjectures were disproved by Thomason and Sidorenko, respectively. A classification of graphs whose number of monochromatic copies is minimized by the random 2-edge-coloring, which are referred to as common graphs, remains a challenging open problem. If Sidorenko's Conjecture, one of the most significant open problems in extremal graph theory, is true, then every 2-chromatic graph is common, and in fact, no 2-chromatic common graph unsettled for Sidorenko's Conjecture is known. While examples of 3-chromatic common graphs were known for a long time, the existence of a 4-chromatic common graph was open until 2012, and no common graph with a larger chromatic number is known. We construct connected k-chromatic common graphs for every k. This answers a question posed by Hatami, Hladký, Král', Norine and Razborov [Combin. Probab. Comput. 21 (2012), 734-742], and a problem listed by Conlon, Fox and Sudakov [London Math. Soc. Lecture Note Ser. 424 (2015), 49-118, Problem 2.28]. This also answers in a stronger form the question raised by Jagger, Št'ovíček and Thomason [Combinatorica 16, (1996), 123-131] whether there exists a common graph with chromatic number at least four.

A graph H is common if the number of monochromatic copies of H in a 2-edge-coloring of the complete graph is asymptotically minimized by the random coloring. The classification of common graphs is one of the most intriguing problems in extremal graph theory. We study the notion of weakly locally common graphs considered by Csóka, Hubai and Lovász [arXiv:1912.02926], where the graph is required to be the minimizer with respect to perturbations of the random 2-edge-coloring. We give a complete analysis of the 12 initial terms in the Taylor series determining the number of monochromatic copies of H in such perturbations and classify graphs H based on this analysis into three categories: • graphs of Class I are weakly locally common, • graphs of Class II are not weakly locally common, and • graphs of Class III cannot be determined to be weakly locally common or not based on the initial 12 terms. As a corollary, we obtain new necessary conditions on a graph to be common and new sufficient conditions on a graph to be not common.

For a real constant α, let $\pi _3^\alpha (G)$ be the minimum of twice the number of K2’s plus α times the number of K3’s over all edge decompositions of G into copies of K2 and K3, where Kr denotes the complete graph on r vertices. Let $\pi _3^\alpha (n)$ be the maximum of $\pi _3^\alpha (G)$ over all graphs G with n vertices.The extremal function $\pi _3^3(n)$ was first studied by Győri and Tuza (Studia Sci. Math. Hungar.22 (1987) 315–320). In recent progress on this problem, Král’, Lidický, Martins and Pehova (Combin. Probab. Comput.28 (2019) 465–472) proved via flag algebras that$\pi _3^3(n) \le (1/2 + o(1)){n^2}$. We extend their result by determining the exact value of $\pi _3^\alpha (n)$ and the set of extremal graphs for all α and sufficiently large n. In particular, we show for α = 3 that Kn and the complete bipartite graph ${K_{\lfloor n/2 \rfloor,\lceil n/2 \rceil }}$ are the only possible extremal examples for large n.

We show that for every sufficiently largen, the number of monotone subsequences of length four in a permutation onnpoints is at least\begin{equation*} \binom{\lfloor{n/3}\rfloor}{4} + \binom{\lfloor{(n+1)/3}\rfloor}{4} + \binom{\lfloor{(n+2)/3}\rfloor}{4}. \end{equation*}Furthermore, we characterize all permutations on [n] that attain this lower bound. The proof uses the flag algebra framework together with some additional stability arguments. This problem is equivalent to some specific type of edge colourings of complete graphs with two colours, where the number of monochromaticK4is minimized. We show that all the extremal colourings must contain monochromaticK4only in one of the two colours. This translates back to permutations, where all the monotone subsequences of length four are all either increasing, or decreasing only.

An exact identity for nonlinear sound wave propagation in one-dimensional media is shown to apply under a wide variety of conditions. The evidence suggests that this is true whenever there is a single input and output channel on each side of the medium, which can generally be achieved using monochromatic filters. It is shown mathematically that the identity cannot be derived from this condition and the known symmetries of the system. The question of what hidden symmetries in the system lead to the identity, and whether it applies even more generally to light waves, remains unresolved.

ATHENA (Advanced Telescope for High-ENergy Astrophysics) is the next high-energy astrophysical mission of the European Space Agency. Media Lario leads an industrial and scientific team that has developed a process to align and integrate more than 700 silicon pore optics mirror modules into the ATHENA X-ray telescope. The process is based on the ultra-violet imaging at 218 nm of each mirror module on the focal plane of a 12 m focal length optical bench. Specifically, the position of the centroid of the point spread function produced by each mirror module when illuminated by a collimated plane is used to align each mirror module. Experimental integration tests and correlation with X-ray measurement at the PANTER test facility in Münich have demonstrated that this process meets the accuracy requirement. This technique allows arbitrary integration sequence and mirror module exchangeability. Moreover, it enables monitoring the telescope point spread function during the integration phase.

The ATHENA (Advanced Telescope for High Energy Astrophysics) X-ray observatory is an ESA-selected L2 class mission. In the proposed configuration, the optical assembly has a diameter of 2.2 m with an effective area of 1.4 m 2 at 1 keV, 0.25 m 2 at 6 keV, and requires an angular resolution of 5 arcsec. To meet the requirements of effective area and angular resolution, the technology of Silicon Pore Optics (SPO) was selected for the optics implementation. The ATHENA's optic assembly requires hundreds of SPOs mirror modules (MMs), obtained by stacking wedged and ribbed silicon wafer plates onto silicon mandrels to form the Wolter-I configuration. Different factors can contribute to limit the imaging performances of SPOs, such as i) diffraction through the pore apertures, ii) plate deformations due to fabrication errors and surface roughness, iii) alignment errors among plates in an MM, and iv) co-focality errors within the MMs assembly. In order to determine the fabrication and assembling tolerances, the impact of these contributions needs to be assessed prior to manufacturing. A set of simulation tools responding to this need was developed in the framework of the ESA-financed projects SIMPOSIuM and ASPHEA. In this paper, we present the performance simulation obtained for the recentlyproposed ATHENA configuration in terms of effective area, and we provide a simulation of the diffractive effects in a pair of SPO MMs. Finally, we present an updated sizing of magnetic diverter (a Halbach array) and the magnetic fields levels that can be reached in order to deviate the most energetic protons out of the detector field.

We have applied the quantum master equation to simulate a two-level system driven by a fractal noise in a dissipative environment. The fractal noise is assumed to be a two-state process with "D and characterized by its correlation function 1rt b where 0 -b -1. Steady state absorption spectrum for the system is obtained analytically for a monochromatic laser excitation. A dramatic blue shift as well as a broadening of the absorption peak, due to the interference between the fractal noise and the natural damping, is observed.

An infinite graph is highly connected if the complement of any subgraph of smaller size is connected. We consider weaker versions of Ramsey's Theorem asserting that in any coloring of the edges of a complete graph there exist large highly connected subgraphs all of whose edges are colored by the same color.

We investigate the distributions of the number of: (1) monochromatic complete subgraphs over edgewise 2-colorings of complete graphs; and (2) monochromatic arithmetic progressions over 2colorings of intervals, as statistical Ramsey theory questions. We present convincing evidence that both distributions are very well-approximated by the Delaporte distribution.

We show that √ k • r k/2 is a threshold interval length where, under mild conditions, almost every r-coloring of an interval of longer length contains a monochromatic k-term arithmetic progression, while almost no r-coloring of an interval of shorter length contains a monochromatic k-term arithmetic progression.

Let r and k be positive integers with r | k. Denote by w z (k; r) the minimum integer such that every coloring χ : [1, w z (k; r)] → {0, 1, . . . , r -1} admits a k-term arithmetic progression a, a + d, . . . , a + (k -1)d with k-1 j=0 χ(a + jd) ≡ 0 (mod r). We investigate these numbers as well as a "mixed" monochromatic/zero-sum analogue. We also present an interesting reciprocity between the van der Waerden numbers and w z (k; r).

We prove that the minimum number (asymptotically) of monochromatic Schur triples that a 2-coloring of [1, n] can have is n 2 22 + O(n). This revised version fills in a minor and subtle gap discovered by M. Primak. (The revision also corrects (at no extra cost) a discrepancy between the solution in the paper and the solution obtained by Maple. In the paper H 1/2 should be H 0 and H 1 should be H 1/2 for the solutions to agree.) This article is accompanied by the Maple package RON, available from either author's website. Tianjin, June 29, 1996: In a fascinating invited talk at the SOCA 96 combinatorics conference organized by Bill Chen, Ron Graham proposed (see also [GRR], p. 390): Problem ($100): Find (asymptotically) the least number of monochromatic Schur triples {i, j, i+ j} that may occur in a 2-coloring of the integers 1, 2, . . . , n.

Let a and b be positive integers such that a ≤ b and (a, b) = (1, 1). We prove that there exists a 6-coloring of the positive integers that does not contain a monochromatic (a, b)-triple, that is, a triple (x, y, z) of positive integers such that y = ax + d and z = bx + 2d for some positive integer d. This confirms a conjecture of Landman and Robertson.

A sequence of positive integers w 1 , w 2 , . . . , w n is called an ascending wave if w i+1w i ≥ w iw i-1 for 2 ≤ i ≤ n -1. For integers k, r ≥ 1, let AW (k; r) be the least positive integer such that under any r-coloring of [1, AW (k; r)] there exists a k-term monochromatic ascending wave. The existence of AW (k; r) is guaranteed by van der Waerden's theorem on arithmetic progressions since an arithmetic progression is, itself, an ascending wave. Originally, Brown, Erdős, and Freedman defined such sequences and proved that k 2k + 1 ≤ AW (k; 2) ≤ 1 3 (k 3 -4k + 9). Alon and Spencer then showed that AW (k; 2) = Θ(k 3 ). In this article, we show that AW (k; 3) = Θ(k 5 ) as well as offer a proof of the existence of AW (k; r) independent of van der Waerden's theorem. Furthermore, we prove that for any > 0 and any fixed r ≥ 1, which, in particular, improves upon the best known upper bound for AW (k; 2). Additionally, we show that for fixed k ≥ 3, AW (k; r) ≤ 2 k-2 (k -1)! r k-1 (1 + o(1)).

This article documents my journey down the rabbit hole, chasing what I have come to know as a particularly unyielding problem in Ramsey theory on the integers: the 2-Large Conjecture. This conjecture states that if D ✓ Z + has the property that every 2-coloring of Z + admits arbitrarily long monochromatic arithmetic progressions with common di↵erence from D then the same property holds for any finite number of colors. We hope to provide a roadmap for future researchers and also provide some new results related to the 2-Large Conjecture. 1. Prologue. Mathematicians tend not to write of their failures. This is rather unfortunate as there are surely countless creative ideas that have never seen the light of day; I have long believed that a Journal of Failed Attempts should exist. My goal with this article is 3-fold: (1) a chronicle of my battle with what I consider a particularly di cult conjecture; (2) to present my progress on this conjecture; and (3) to provide a roadmap to those who want to take on this challenging conjecture. The majority of this work took place over the course of a year, circa 2010 1 . Since that time I have frequently revisited this intriguing problem, even though that year was mostly an exercise in banging my head against various brick walls. I wish I knew how to quit it. I love this conjecture, so much so that I've followed it down the rabbit hole. However, if we are to take away one message from Steinbeck's Of Mice and Men, it's that sometimes the rabbit doesn't love you back. 2. What's Up, Doc? Ramsey theory may best be summed up as "the study of the preservation of structures under set partitions" 1991 AMS Mathematics subject classification. 05D10. Keywords and phrases. 2-Large conjecture, arithmetic progressions, van der Waerden .

Let r and k be positive integers with r | k. Denote by w z (k; r) the minimum integer such that every coloring χ : [1, w z (k; r)] → {0, 1, . . . , r -1} admits a k-term arithmetic progression a, a + d, . . . , a + (k -1)d with k-1 j=0 χ(a + jd) ≡ 0 (mod r). We investigate these numbers as well as a "mixed" monochromatic/zero-sum analogue. We also present an interesting reciprocity between the van der Waerden numbers and w z (k; r).

We investigate the distributions of the number of: (1) monochromatic complete subgraphs over edgewise 2-colorings of complete graphs; and (2) monochromatic arithmetic progressions over 2colorings of intervals, as statistical Ramsey theory questions. We present convincing evidence that both distributions are very well-approximated by the Delaporte distribution.

We show that √ k • r k/2 is a threshold interval length where, under mild conditions, almost every r-coloring of an interval of longer length contains a monochromatic k-term arithmetic progression, while almost no r-coloring of an interval of shorter length contains a monochromatic k-term arithmetic progression.

A sequence of positive integers w 1 , w 2 , . . . , w n is called an ascending wave if w i+1w i ≥ w iw i-1 for 2 ≤ i ≤ n -1. For integers k, r ≥ 1, let AW (k; r) be the least positive integer such that under any r-coloring of [1, AW (k; r)] there exists a k-term monochromatic ascending wave. The existence of AW (k; r) is guaranteed by van der Waerden's theorem on arithmetic progressions since an arithmetic progression is, itself, an ascending wave. Originally, Brown, Erdős, and Freedman defined such sequences and proved that k 2 -k +1 ≤ AW (k; 2) ≤ 1 3 (k 3 -4k + 9). Alon and Spencer then showed that AW (k; 2) = Θ(k 3 ). In this article, we show that AW (k; 3) = Θ(k 5 ) as well as offer a proof of the existence of AW (k; r) independent of van der Waerden's theorem. Furthermore, we prove that for any > 0 and any fixed r ≥ 1, which, in particular, improves upon the best known upper bound for AW (k; 2). Additionally, we show that for fixed k ≥ 3,

For integers n ≥ 1 and k ≥ 0, let M k (n) represent the minimum number of monochromatic solutions to x + y < z over all 2-colorings of {k + 1, k + 2, . . . , k + n} . We show that for any 2) 2 ≈ .005686. A structural result is also proven, which can be used to determine the exact value of M k (n) for given k and n.

The response function of a high-resolution high-energy photon spectrometer (HHS), consisting of a twin Ge detector and BGO (Bi 3 Ge 4 O 12 ) anti-coincidence shields, has been measured for 10.763 MeV monochromatic g-rays generated in a resonant reaction 27 Al(p,g) 28 Si. The experimental response functions measured with and without the anti-coincidence were compared with results by Monte Carlo simulations, in which a pulse-height degradation effect associated with a surface channel of the twin Ge detector has been included. Excellent agreement was obtained between the experimental response functions and the simulations.

X-ray fluorescence spectrometry (x.r.f.) can be done through excitation with synchrotron radiation. This permits multi-element determinations in the trace region with improved detection limits compared to conventional x.r.f. Detection limits are evaluated and compared with theoretically calculated values. For a beam diameter of 0.5 mm and a sample of 1 mg cm", absolute detection limits are between 0.1 and 0.4 pg. The dependence of the detection limit on the atomic number is reduced, when white synchrotron radiation is used for excitation instead of monochromatic radiation. The optimum of the limit of detection on the Z-scale can be shifted to higher atomic numbers and improved through filtration of the primary radiation by aluminium absorbers. Preparation of samples on different polymeric films is discussed in relation to blank values.

In recent years, the demand for hyperspectral imaging devices has grown significantly, driven by their ability of capturing high-resolution spectral information. Among the several possible optical designs for acquiring hyperspectral images, there is a growing interest in interferometric spectral imaging systems based on division of aperture. These systems have the advantage of capturing snapshot acquisitions while maintaining a compact design. However, they require a careful calibration to operate properly. In this work, we present the interferometer response characterization algorithm (IRCA), a robust three-step procedure designed to characterize the transmittance response of multi-aperture imaging spectrometers based on the interferometry of Fabry-Perot. Additionally, we propose a formulation of the image formation model for such devices suitable to estimate the parameters of interest by considering the model under various regimes of finesse. The proposed algorithm processes the image output obtained from a set of monochromatic light sources and refines the results using nonlinear regression after an ad-hoc initialization. Through experimental analysis conducted on four different prototypes from the Image SPectrometer On Chip (ImSPOC) family, we validate the performance of our approach for characterization. The associated source code for this paper is available at .