Статті в журналах: "ENERGY MATRICES"

1

Bravo, Diego, Florencia Cubría, and Juan Rada. "Energy of matrices." Applied Mathematics and Computation 312 (November 2017): 149–57. http://dx.doi.org/10.1016/j.amc.2017.05.051.

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2

Kharaghani, H., and B. Tayfeh-Rezaie. "On the energy of (0,1)-matrices." Linear Algebra and its Applications 429, no. 8-9 (October 2008): 2046–51. http://dx.doi.org/10.1016/j.laa.2008.06.001.

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3

Borodin, Alexei, and Sylvia Serfaty. "Renormalized Energy Concentration in Random Matrices." Communications in Mathematical Physics 320, no. 1 (April 16, 2013): 199–244. http://dx.doi.org/10.1007/s00220-013-1716-z.

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4

Nikiforov, Vladimir. "The energy of graphs and matrices." Journal of Mathematical Analysis and Applications 326, no. 2 (February 2007): 1472–75. http://dx.doi.org/10.1016/j.jmaa.2006.03.072.

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5

Nikiforov, Vladimir. "Graphs and matrices with maximal energy." Journal of Mathematical Analysis and Applications 327, no. 1 (March 2007): 735–38. http://dx.doi.org/10.1016/j.jmaa.2006.03.089.

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6

Tafrikan, Mohammad, and Mohammad Ghani. "Iterative Method of Thomas Algorithm on The Case Study of Energy Equation." Postulat : Jurnal Inovasi Pendidikan Matematika 3, no. 1 (July 26, 2022): 14. http://dx.doi.org/10.30587/postulat.v3i1.4346.

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Implicit method is one of the finite difference method and is widely used for discretization some of ordinary or partial differential equations, such like: advection equation, heat transfer equation, burger equation, and many others. Implicit method is unconditionally stable and has been proved with the approximation of Von-Neumann stability criterion. Actually, implicit method is always identical to block matrices (tri-diagonal matrices or penta-diagonal matrices). These matrices can be solved numerically by Thomas algorithm including Gauss elimination using pivot or not, backward or forward substitution. Furthermore, it can be also solved using LU decomposition method with the elimination of lower triangle matrices first and then the elimination of upper triangle matrices. In this research, Thomas algorithm is used to solve numerically for the problem of convective flow on boundary layer, especially for energy equation with the variation of Prandtl number ( ).

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7

Gutman, Ivan. "Spectrum and energy of the Sombor matrix." Vojnotehnicki glasnik 69, no. 3 (2021): 551–61. http://dx.doi.org/10.5937/vojtehg69-31995.

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Introduction/purpose: The Sombor matrix is a vertex-degree-based matrix associated with the Sombor index. The paper is concerned with the spectral properties of the Sombor matrix. Results: Equalities and inequalities for the eigenvalues of the Sombor matrix are obtained, from which two fundamental bounds for the Sombor energy (= energy of the Sombor matrix) are established. These bounds depend on the Sombor index and on the "forgotten" topological index. Conclusion: The results of the paper contribute to the spectral theory of the Sombor matrix, as well as to the general spectral theory of matrices associated with vertex-degree-based graph invariants.

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8

Godsi, Oded, Christian R. Evenhuis, and Michael A. Collins. "Interpolation of multidimensional diabatic potential energy matrices." Journal of Chemical Physics 125, no. 10 (September 14, 2006): 104105. http://dx.doi.org/10.1063/1.2338912.

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9

Bofill, Josep Maria, Àngels Povill, and Jaime Rubio. "Energy partitioning using two-electron average matrices." Chemical Physics Letters 222, no. 1-2 (May 1994): 51–57. http://dx.doi.org/10.1016/0009-2614(94)00322-x.

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10

Muratova, E. N., and A. A. Shemukhin. "Nanoscale matrices to transport high-energy beams." Journal of Physics: Conference Series 917 (November 2017): 092016. http://dx.doi.org/10.1088/1742-6596/917/9/092016.

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11

Bourgade, Paul, Laszlo Erdős, Horng-Tzer Yau, and Jun Yin. "Fixed Energy Universality for Generalized Wigner Matrices." Communications on Pure and Applied Mathematics 69, no. 10 (December 15, 2015): 1815–81. http://dx.doi.org/10.1002/cpa.21624.

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12

Li, Cai Zhen, Fei Liu, Cong Bo Li, and Qiu Lian Wang. "Analysis Model for Energy Consumption in Manufacturing Enterprises Based on Input-Output Theory and its Applications." Applied Mechanics and Materials 16-19 (October 2009): 1058–63. http://dx.doi.org/10.4028/www.scientific.net/amm.16-19.1058.

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Анотація:

Analysis of energy consumption which could explore energy saving potential is of important significance for energy saving in manufacturing enterprises. An analysis model including physical and monetary input-output models for energy consumption in manufacturing enterprises based on input-output theory is constructed. Physical and monetary energy consumption coefficient matrices are obtained from the analysis model. Then, some application ideas are proposed, including vertical and horizontal comparison of coefficient matrices elements of a manufacturing enterprise in per unit time, comparison of coefficient matrices elements of a manufacturing enterprise in different unit times, comparison of coefficient matrices elements of manufacturing enterprises within the same industry in per unit time, effect analysis of energy price change to energy consumption of a manufacturing enterprise. Finally, a case study of a heavy-machinery manufacturing enterprises validates its practicability.

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13

Tretyakov, Ilya V., Tuyara V. Petrova, Aleksey V. Kireynov, Roman A. Korokhin, Elena O. Platonova, Olga V. Alexeeva, Yulia A. Gorbatkina, Vitaliy I. Solodilov, Gleb Yu Yurkov, and Alexander Al Berlin. "Fracture of Epoxy Matrixes Modified with Thermo-Plastic Polymers and Winding Glass Fibers Reinforced Plastics on Their Base under Low-Velocity Impact Condition." Polymers 15, no. 13 (July 5, 2023): 2958. http://dx.doi.org/10.3390/polym15132958.

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The work is aimed at studying the impact resistance of epoxy oligomer matrices (EO) modified with polysulfone (PSU) or polyethersulfone (PES) and glass fibers reinforced plastics (GFRP) based on them under low-velocity impact conditions. The concentration dependences of strength and fracture energy of modified matrices and GFRP were determined. It has been determined that the type of concentration curves of the fracture energy of GFRP depends on the concentration and type of the modifying polymer. It is shown that strength σ and fracture energy EM of thermoplastic-modified epoxy matrices change little in the concentration range from 0 to 15 wt.%. However, even with the introduction of 20 wt.% PSU into EO, the strength increases from 164 MPa to 200 MPa, and the fracture energy from 32 kJ/m2 to 39 kJ/m2. The effect of increasing the strength and fracture energy of modified matrices is retained in GFRP. The maximum increase in shear strength (from 72 MPa to 87 MPa) is observed for GFRP based on the EO + 15 wt.% PSU matrix. For GFRP based on EO + 20 wt.% PES, the shear strength is reduced to 69 MPa. The opposite effect is observed for the EO + 20 wt.% PES matrix, where the strength value decreases from 164 MPa to 75 MPa, and the energy decreases from 32 kJ/m2 to 10 kJ/m2. The reference value for the fracture energy of GFRP 615 is 741 kJ/m2. The maximum fracture energy for GFRP is based on EO + 20 wt.% PSU increases to 832 kJ/m2 for GFRP based on EO + 20 wt.% PES—up to 950 kJ/m2. The study of the morphology of the fracture surfaces of matrices and GFRP confirmed the dependence of impact characteristics on the microstructure of the modified matrices and the degree of involvement in the process of crack formation. The greatest effect is achieved for matrices with a phase structure “thermoplastic matrix-epoxy dispersion.” Correlations between the fracture energy and strength of EO + PES matrices and GFRP have been established.

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14

OBOUDI, MOHAMMAD REZA. "LOWER BOUNDS FOR ENERGY OF MATRICES AND ENERGY OF REGULAR GRAPHS." Kragujevac Journal of Mathematics 46, no. 5 (2022): 701–9. http://dx.doi.org/10.46793/kgjmat2205.701o.

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15

Mahato, Iswar, and M. Rajesh Kannan. "Eccentricity energy change of complete multipartite graphs due to edge deletion." Special Matrices 10, no. 1 (January 1, 2022): 193–202. http://dx.doi.org/10.1515/spma-2021-0156.

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Abstract The eccentricity matrix ɛ(G) of a graph G is obtained from the distance matrix of G by retaining the largest distances in each row and each column, and leaving zeros in the remaining ones. The eccentricity energy of G is sum of the absolute values of the eigenvalues of ɛ(G). Although the eccentricity matrices of graphs are closely related to the distance matrices of graphs, a number of properties of eccentricity matrices are substantially different from those of the distance matrices. The change in eccentricity energy of a graph due to an edge deletion is one such property. In this article, we give examples of graphs for which the eccentricity energy increase (resp., decrease) but the distance energy decrease (resp., increase) due to an edge deletion. Also, we prove that the eccentricity energy of the complete k-partite graph Kn 1, ... , nk with k ≥ 2 and ni ≥ 2, increases due to an edge deletion.

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16

Pan, Wen Jun, and Zhi Wu Wei. "Reckoning for Element Characteristics Matrix of Space Timoshenko-Beam Based on Energy Variational Principle." Applied Mechanics and Materials 66-68 (July 2011): 1356–61. http://dx.doi.org/10.4028/www.scientific.net/amm.66-68.1356.

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To analyze and calculate the element characteristics matrices of space Timoshenko-beam, research work were carried out on the basis of energy variational principle. Displacement function for the space Timoshenko-beam were put forward, the expressions for element mass matrix, stiffness matrix and load array were deduced by energy functional extremum, and the explicit forms of element mass and stiffness matrices were integrated finally. Results show that the element mass and stiffness matrices computed by this method are consistent with those in related references. It has a good theoretical and practical value in the calculation for characteristics matrices of other elements.

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17

Hebert, T., H. Wiggenhauser, and D. M. Kolb. "Energy transfer in silver‐doped rare gas matrices." Journal of Chemical Physics 91, no. 3 (August 1989): 1417–22. http://dx.doi.org/10.1063/1.457101.

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18

Hybertsen, Mark S., and Steven G. Louie. "Model dielectric matrices for quasiparticle self-energy calculations." Physical Review B 37, no. 5 (February 15, 1988): 2733–36. http://dx.doi.org/10.1103/physrevb.37.2733.

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19

Nikiforov, V. "Beyond graph energy: Norms of graphs and matrices." Linear Algebra and its Applications 506 (October 2016): 82–138. http://dx.doi.org/10.1016/j.laa.2016.05.011.

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20

Poppe, R. "Empirical corrections of energy matrices in atomic spectra." Physica B+C 132, no. 3 (September 1985): 377–87. http://dx.doi.org/10.1016/0378-4363(85)90124-x.

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21

Guzmán, Johnny, and Caroline Klivans. "Chip-firing and energy minimization on M-matrices." Journal of Combinatorial Theory, Series A 132 (May 2015): 14–31. http://dx.doi.org/10.1016/j.jcta.2014.12.002.

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22

Lukin, L. V. "Thermalization of low energy electrons in hydrocarbon matrices." International Journal of Radiation Applications and Instrumentation. Part C. Radiation Physics and Chemistry 40, no. 6 (December 1992): 565–73. http://dx.doi.org/10.1016/1359-0197(92)90225-5.

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23

Rajesh Kanna, M. R., R. Pradeep Kumar, Soner Nandappa, and Ismail Naci Cangul. "On Solutions of Fractional order Telegraph Partial Differential Equation by Crank-Nicholson Finite Difference Method." Applied Mathematics and Nonlinear Sciences 5, no. 2 (August 10, 2020): 85–98. http://dx.doi.org/10.2478/amns.2020.2.00017.

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Анотація:

AbstractThree main tools to study graphs mathematically are to make use of the vertex degrees, distances and matrices. The classical graph energy was defined by means of the adjacency matrix in 1978 by Gutman and has a large number of applications in chemistry, physics and related areas. As a result of its importance and numerous applications, several modifications of the notion of energy have been introduced since then. Most of them are defined by means of graph matrices constructed by vertex degrees. In this paper we define another type of energy called q-distance energy by means of distances and matrices. We study some fundamental properties and also establish some upper and lower bounds for this new energy type.

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24

Berman, Abraham, and Robert Grone. "Bipartite completely positive matrices." Mathematical Proceedings of the Cambridge Philosophical Society 103, no. 2 (March 1988): 269–76. http://dx.doi.org/10.1017/s0305004100064835.

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A non-zero n-by-n matrix A is said to be completely positive if there exist non-negative vectors b1,…, bk, such thatThe smallest such integer k is called the factorization index of (completely positive) A, and is denoted by ø(A). Completely positive matrices are important in the study of block designs [4], statistics and modelling of energy demand [3].

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25

Chu, Zheng-Qing, Jia-Bao Liu, and Xiao-Xin Li. "The Laplacian-Energy-Like Invariants of Three Types of Lattices." Journal of Analytical Methods in Chemistry 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/7320107.

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This paper mainly studies the Laplacian-energy-like invariants of the modified hexagonal lattice, modified Union Jack lattice, and honeycomb lattice. By utilizing the tensor product of matrices and the diagonalization of block circulant matrices, we derive closed-form formulas expressing the Laplacian-energy-like invariants of these lattices. In addition, we obtain explicit asymptotic values of these invariants with software-aided computations of some integrals.

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26

Pal, Piyush, Suresh Kumar Patel, Ajaya Bharti, Audhesh Narayan, Rahul Dev, and Dhananjay Singh. "Energy, exergy, energy matrices, exergoeconomic and enviroeconomic assessment of modified solar stills." Sustainable Energy Technologies and Assessments 47 (October 2021): 101514. http://dx.doi.org/10.1016/j.seta.2021.101514.

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27

Nagarajan, D., and A. Rameshkumar. "VARIOUS KINDS OF MATRICES IN CYCLOTOMIC GRAPHS." Advances in Mathematics: Scientific Journal 10, no. 12 (December 10, 2021): 3579–96. http://dx.doi.org/10.37418/amsj.10.12.5.

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The component matrix, Laplacian matrix, Distance matrix, Peripheral distance matrix, Distance Laplacian of the cyclotomic graphs and some properties are found. The D-energy, $D_{p}$-energy, $D^{L}$-energy and some indices of the cyclotomic graphs are determined. For the real symmetric matrices, matrices that attain the maximum $L, L_{s}$ and the minimum S are calculated. The Hausdorff distance and optimal matching distance of the cyclotomic graphs are evaluated.

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28

CHATURVEDI, S., V. GUPTA, and G. SÁNCHEZ-COLÓN. "BOUNDS ON QUARK MASS MATRICES ELEMENTS DUE TO MEASURED PROPERTIES OF THE MIXING MATRIX AND PRESENT VALUES OF THE QUARK MASSES." International Journal of Modern Physics A 23, no. 11 (April 30, 2008): 1729–46. http://dx.doi.org/10.1142/s0217751x0803975x.

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We obtain constraints on possible structures of mass matrices in the quark sector by using as experimental restrictions the determined values of the quark masses at the MZ energy scale, the magnitudes of the quark mixing matrix elements V ud , V us , V cd and V cs , and the Jarlskog invariant J(V). Different cases of specific mass matrices are examined in detail. The quality of the fits for the Fritzsch- and Stech-type mass matrices is about the same with χ2/ d.o.f. = 4.23/3 = 1.41 and χ2/ d.o.f. = 9.10/4 = 2.28, respectively. The fit for a simple generalization (one extra parameter) of the Fritzsch type matrices, in the physical basis, is much better with χ2/ d.o.f. = 1.89/4 = 0.47. For comparison we also include the results using the quark masses at the 2 GeV energy scale. The fits obtained at this energy scale are similar to that at MZ energy scale, implying that our results are unaffected by the evolution of the quark masses from 2 to 91 GeV.

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29

Ellwood, Ian T. "Relating branes and matrices." Journal of High Energy Physics 2005, no. 08 (August 23, 2005): 078. http://dx.doi.org/10.1088/1126-6708/2005/08/078.

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30

Cornalba, Lorenzo, and Washington Taylor. "Holomorphic curves from matrices." Nuclear Physics B 536, no. 3 (December 1998): 513–52. http://dx.doi.org/10.1016/s0550-3213(98)00702-0.

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31

Fring, A., and C. Korff. "Colour valued scattering matrices." Physics Letters B 477, no. 1-3 (March 2000): 380–86. http://dx.doi.org/10.1016/s0370-2693(00)00226-4.

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32

AHN, CHANGRIM, and DIEGO BOMBARDELLI. "EXACT S-MATRICES FOR AdS3/CFT2." International Journal of Modern Physics A 28, no. 32 (December 30, 2013): 1350168. http://dx.doi.org/10.1142/s0217751x13501686.

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We propose exact S-matrices for the AdS 3/ CFT 2 duality between type IIB strings on AdS 3×S3×M4 with M4 = S3×S1 or T4 and the corresponding two-dimensional conformal field theories. We fix the two-particle S-matrices on the basis of the symmetries su(1|1) and su(1|1)×su(1|1). A crucial justification comes from the derivation of the all-loop Bethe ansatz matching exactly the recent conjecture proposed by Babichenko et al. [J. High Energy Phys.1003, 058 (2010), arXiv:0912.1723 [hep-th]] and Ohlsson Sax and Stefanski, Jr. [J. High Energy Phys.1108, 029 (2011), arXiv:1106.2558 [hep-th]].

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33

Sergeev, S. M. "Two-Dimensional R-Matrices — Descendants of Three-Dimensional R-Matrices." Modern Physics Letters A 12, no. 19 (June 21, 1997): 1393–410. http://dx.doi.org/10.1142/s0217732397001424.

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Finite layers of three-dimensional models can be regarded as two-dimensional with complicated multi-stated weights. The tetrahedron equation in 3D provides the Yang–Baxter equation for this composite weights in 2D. Such solutions of the Yang–Baxter equation are constructed for the simplest operator solution of the tetrahedron equation. These R-matrices can be regarded as a special projection of universal R-matrix for some Drinfeld double [Formula: see text], associated with the affine algebra [Formula: see text]. Usual R-matrix for [Formula: see text] is another projection of [Formula: see text].

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34

Crépin, C., F. Legay, N. Legay-Sommaire, and A. Tramer. "Electronic to vibrational energy transfer and relaxation in matrices. II. Hg in mixed N2/Kr matrices." Chemical Physics 111, no. 2 (January 1987): 183–91. http://dx.doi.org/10.1016/0301-0104(87)80133-7.

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35

Nikiforov, V., and N. Agudelo. "On the minimum trace norm/energy of (0,1)-matrices." Linear Algebra and its Applications 526 (August 2017): 42–59. http://dx.doi.org/10.1016/j.laa.2017.03.024.

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36

Bordenave, Charles, and Alice Guionnet. "Delocalization at Small Energy for Heavy-Tailed Random Matrices." Communications in Mathematical Physics 354, no. 1 (May 23, 2017): 115–59. http://dx.doi.org/10.1007/s00220-017-2914-x.

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37

Kiel, Christina, and Luis Serrano. "Prediction of Ras-effector interactions using position energy matrices." Bioinformatics 23, no. 17 (June 28, 2007): 2226–30. http://dx.doi.org/10.1093/bioinformatics/btm336.

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38

Bochicchio, Roberto C., and Diego Rial. "Note: Energy convexity and density matrices in molecular systems." Journal of Chemical Physics 137, no. 22 (December 14, 2012): 226101. http://dx.doi.org/10.1063/1.4771955.

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39

Harriman, John E. "Kinetic energy matrices in a basis of equidensity orbitals." Journal of Chemical Physics 104, no. 15 (April 15, 1996): 5912–21. http://dx.doi.org/10.1063/1.471323.

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40

Go, Liew Chien, Dhan Lord B. Fortela, Emmanuel Revellame, Mark Zappi, William Chirdon, William Holmes, and Rafael Hernandez. "Biobased chemical and energy recovered from waste microbial matrices." Current Opinion in Chemical Engineering 26 (December 2019): 65–71. http://dx.doi.org/10.1016/j.coche.2019.08.005.

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41

OZ, Mert Sinan. "Coefficients of Randic and Sombor characteristic polynomials of some graph types." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 71, no. 3 (September 30, 2022): 778–90. http://dx.doi.org/10.31801/cfsuasmas.1080426.

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Анотація:

Let GG be a graph. The energy of GG is defined as the summation of absolute values of the eigenvalues of the adjacency matrix of GG. It is possible to study several types of graph energy originating from defining various adjacency matrices defined by correspondingly different types of graph invariants. The first step is computing the characteristic polynomial of the defined adjacency matrix of GG for obtaining the corresponding energy of GG. In this paper, formulae for the coefficients of the characteristic polynomials of both the Randic and the Sombor adjacency matrices of path graph PnPn , cycle graph CnCn are presented. Moreover, we obtain the five coefficients of the characteristic polynomials of both Randic and Sombor adjacency matrices of a special type of 3−regular graph RnRn.

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42

Kharchenko, Vladyslav F. "Partial wave off-shell Coulomb amplitudes at excited-state energy." Canadian Journal of Physics 96, no. 8 (August 2018): 933–37. http://dx.doi.org/10.1139/cjp-2017-0677.

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Based on the integral representation of the three-dimensional Coulomb transition matrix elaborated by us formerly with the use of specific symmetry of the interaction in the four-dimensional Euclidean space introduced by Fock, the possibility of analytical solution of the integral equation for the partial wave transition matrices at the excited bound state energy has been studied. New analytical expressions for the partial s-, p-, and d-wave Coulomb t-matrices for like-charged particles and the expression for the partial d-wave t-matrix for unlike-charged particles at the energy of the first excited bound state have been derived.

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43

Vaandrager, P., and S. A. Rakityansky. "Extracting the resonance parameters from experimental data on scattering of charged particles." International Journal of Modern Physics E 25, no. 02 (February 2016): 1650014. http://dx.doi.org/10.1142/s0218301316500142.

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Анотація:

A new parametrization of the multi-channel [Formula: see text]-matrix is used to fit scattering data and then to locate the resonances as its poles. The [Formula: see text]-matrix is written in terms of the corresponding “in” and “out” Jost matrices which are expanded in the Taylor series of the collision energy [Formula: see text] around an appropriately chosen energy [Formula: see text]. In order to do this, the Jost matrices are written in a semi-analytic form where all the factors (involving the channel momenta and Sommerfeld parameters) responsible for their “bad behavior” (i.e., responsible for the multi-valuedness of the Jost matrices and for branching of the Riemann surface of the energy) are given explicitly. The remaining unknown factors in the Jost matrices are analytic and single-valued functions of the variable [Formula: see text] and are defined on a simple energy plane. The expansion is done for these analytic functions and the expansion coefficients are used as the fitting parameters. The method is tested on a two-channel model, using a set of artificially generated data points with typical error bars and a typical random noise in the positions of the points.

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44

Zechmann, Carsten, Tassilo Muskat, and Jürgen Grotemeyer. "Wavelength- and Time-Resolved Luminescence Spectroscopy for Investigation of the Matrix-Assisted Laser Desorption Process." European Journal of Mass Spectrometry 8, no. 4 (August 2002): 287–93. http://dx.doi.org/10.1255/ejms.490.

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This work deals with investigations of fluorescence phenomena during interaction of ultraviolet laser radiation with four substances (2,5-dihydroxybenzoic acid, 3-hydroxypicolinic acid, dithranol and ferulic acid) commonly used as matrices in matrix-assisted laser desorption/ionization (MALDI). Wavelength-resolved fluorescence measurements allowed classification of UV-MALDI matrices on the basis of their Stokes shift. Matrices showing a high Stokes shift dissipated high amounts of laser energy by means of intra- and intermolecular energy transfer processes, hence contributing less to the ionization of analyte compounds. Conversely, matrix substances with a low Stokes shift retained more of the original photonic energy which may then be available for ionization within the matrix or after desorption of molecular species. Therefore matrix compounds can be designated as “hard” (high ionization energy) in the case of small Stokes shifts or “soft” (low ionization energy) in the case of high Stokes shifts. Time-resolved measurements showed fluorescence lifetimes below 5 ns for all four substances.

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45

Makai, Mihály. "Plane waves and response matrices." Annals of Nuclear Energy 19, no. 10-12 (October 1992): 715–36. http://dx.doi.org/10.1016/0306-4549(92)90014-3.

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46

Oohora, Koji, Tsuyoshi Mashima, Kei Ohkubo, Shunichi Fukuzumi, and Takashi Hayashi. "Energy migration within hexameric hemoprotein reconstituted with Zn porphyrinoid molecules." Chemical Communications 51, no. 55 (2015): 11138–40. http://dx.doi.org/10.1039/c5cc02680f.

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47

Dobkowski, Jacek, Igor V. Sazanovich, Aleksander Gorski, and Jacek Waluk. "Energy Relaxation of Porphycene in Atomic and Molecular Cryogenic Matrices." Photochem 2, no. 2 (April 6, 2022): 299–307. http://dx.doi.org/10.3390/photochem2020021.

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Анотація:

The kinetics of relaxation of high-lying electronic states of porphycene (porphyrin isomer) embedded in different cryogenic matrices were studied using picosecond time-resolved fluorescence (TRF) and transient absorption (TA) techniques. The molecule was excited into the Soret band, i.e., with a large energy excess compared to that of the lowest (Q) excited state. The TRF and TA time profiles obtained for porphycene embedded in argon and methane matrices were remarkably different: the overall relaxation in argon occurred in 64 ps, whereas the corresponding value for methane matrix was 18 ps. Analysis of the evolution over time of different spectral ranges of TRF spectra indicates the multidimensional character of relaxation kinetics.

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48

Rabin, A. V., S. V. Michurin, and V. A. Lipatnikov. "DEVELOPMENT OF A CLASS OF SYSTEM AND RETURN SYSTEM MATRIXES PROVIDING INCREASE IN NOISE IMMUNITY OF SPECTRALLY EFFECTIVE MODULATION SCHEMES ON BASIS OF ORTHOGONAL CODING." Issues of radio electronics, no. 10 (October 20, 2018): 75–79. http://dx.doi.org/10.21778/2218-5453-2018-10-75-79.

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In work it is proposed in the digital systems of messages transmission for noise immunity's increase with the fixed code rate to use an additional coding called by the authors orthogonal. The way of a definition of orthogonal codes is presented, the synthesis algorithm of system and inverse system matrices of orthogonal codes is developed, and the main parameters of some matrices constructed by the offered algorithm are specified. Orthogonal coding as a special case of convolutional coding is defined by matrices, which elements are polynomials in the delay variable with integer coefficients. Code words are given by multiplication of an information polynomial by a system matrix, and decoding is performed by multiplication by an inverse system matrix. Basic ratios for orthogonal coding are given in article, and properties of system and inverse matrices are specified. Parameters of system and inverse system matrices assure additional gain in signal-to-noise ratio. This gain is got as a result of a more effective use of energy of transmitted signals. For transmission of one symbol energy of several symbols is accumulated.

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49

Le Dret, Hervé, and Annie Raoult. "The quasiconvex envelope of the Saint Venant–Kirchhoff stored energy function." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 125, no. 6 (1995): 1179–92. http://dx.doi.org/10.1017/s0308210500030456.

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We give an explicit expression for the quasiconvex envelope of the Saint Venant–Kirchhoff stored energy function in terms of the singular values. This envelope is also the convex, polyconvex and rank 1 convex envelope of the Saint Venant–Kirchhoff stored energy function. Moreover, it coincides with the Saint Venant–Kirchhoff stored energy function itself on, and only on, the set of matrices whose singular values arranged in increasing order are located outside an ellipsoid. It vanishes on, and only on, the set of matrices whose singular values are less than 1. Consequently, a Saint Venant–Kirchhoff material can be compressed under zero external loading.

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50

PAN, FENG, LIAN-RONG DAI, DAN ZHANG, and J. P. DRAAYER. "PERMUTATION GROUP APPROACH TO THE ONE-DIMENSIONAL XXX HEISENBERG OPEN SPIN-1/2 CHAINS." International Journal of Modern Physics C 15, no. 02 (February 2004): 247–65. http://dx.doi.org/10.1142/s0129183104005668.

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Permutation group approach to the one-dimensional XXX Heisenberg open spin-1/2 chain with nearest neighbor interaction is proposed, which is formulated not only for half-filling excitations, but also for general case. Regularity of energy matrices and the corresponding wavefunctions are made up by using an induction method, which makes it possible to study the eigenvalue problem systematically. A Mathematica package for generating the energy matrices is implemented according to this procedure.

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