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Journal articles on the topic 'Condensed Mathematics'

Author: Grafiati

Published: 14 December 2024

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1

Mimouni, Abdeslam. "Condensed and Strongly Condensed Domains." Canadian Mathematical Bulletin 51, no. 3 (September 1, 2008): 406–12. http://dx.doi.org/10.4153/cmb-2008-041-9.

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AbstractThis paper deals with the concepts of condensed and strongly condensed domains. By definition, an integral domain R is condensed (resp. strongly condensed) if each pair of ideals I and J of R, I J = ﹛ab/a ∈ I, b ∈ J﹜ (resp. I J = a J for some a ∈ I or I J = Ib for some b ∈ J). More precisely, we investigate the ideal theory of condensed and strongly condensed domains in Noetherian-like settings, especially Mori and strong Mori domains and the transfer of these concepts to pullbacks.

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2

Anderson, D. D., and Tiberiu Dumitrescu. "Condensed Domains." Canadian Mathematical Bulletin 46, no. 1 (March 1, 2003): 3–13. http://dx.doi.org/10.4153/cmb-2003-001-2.

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AbstractAn integral domain D with identity is condensed (resp., strongly condensed) if for each pair of ideals I, J of D, IJ = {ij ; i ∈ I; j ∈ J} (resp., IJ = iJ for some i ∈ I or IJ = Ij for some j ∈ J). We show that for a Noetherian domain D, D is condensed if and only if Pic(D) = 0 and D is locally condensed, while a local domain is strongly condensed if and only if it has the two-generator property. An integrally closed domain D is strongly condensed if and only if D is a Bézout generalized Dedekind domain with at most one maximal ideal of height greater than one. We give a number of equivalencies for a local domain with finite integral closure to be strongly condensed. Finally, we show that for a field extension k ⊆ K, the domain D = k + XK[[X]] is condensed if and only if [K : k] ≤ 2 or [K : k] = 3 and each degree-two polynomial in k[X] splits over k, while D is strongly condensed if and only if [K : k] ≤ 2.

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3

Salmhofer, Manfred. "Renormalization in condensed matter: Fermionic systems – from mathematics to materials." Nuclear Physics B 941 (April 2019): 868–99. http://dx.doi.org/10.1016/j.nuclphysb.2018.07.004.

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4

Matkowsky, B. J., and V. Volpert. "Spiral Gasless Condensed Phase Combustion." SIAM Journal on Applied Mathematics 54, no. 1 (February 1994): 132–46. http://dx.doi.org/10.1137/s0036139992229253.

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5

Song, Dong, and Bharat Bhushan. "Optimization of bioinspired triangular patterns for water condensation and transport." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 377, no. 2150 (June 10, 2019): 20190127. http://dx.doi.org/10.1098/rsta.2019.0127.

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Water condenses on a surface in ambient environment if the surface temperature is below the dew point. For water collection, droplets should be transported to storage before the condensed water evaporates. In this study, Laplace pressure gradient inspired by conical spines of cactus plants is used to facilitate the transport of water condensed in a triangular pattern to the storage. Droplet condensation, transportation and water collection rate within the bioinspired hydrophilic triangular patterns with various lengths and included angles, surrounded by superhydrophobic regions, were explored. The effect of relative humidity was also explored. This bioinspired technique can be used to develop efficient water collection systems. This article is part of the theme issue ‘Bioinspired materials and surfaces for green science and technology (part 2)’.

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6

Artusa, Marco. "Duality for condensed cohomology of the Weil group of a $p$-adic field." Documenta Mathematica 29, no. 6 (November 26, 2024): 1381–434. http://dx.doi.org/10.4171/dm/977.

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We use the theory of Condensed Mathematics to build a condensed cohomology theory for the Weil group of a p -adic field. The cohomology groups are proved to be locally compact abelian groups of finite ranks in some special cases. This allows us to enlarge the local Tate duality to a more general category of non-necessarily discrete coefficients, where it takes the form of a Pontryagin duality between locally compact abelian groups.

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7

Escudero, Carlos, Filippo Gazzola, Robert Hakl, Ireneo Peral, and Pedro José Torres. "Existence results for a fourth order partial differential equation arising in condensed matter physics." Mathematica Bohemica 140, no. 4 (2015): 385–93. http://dx.doi.org/10.21136/mb.2015.144457.

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8

Anderson, David F., Jimmy T. Arnold, and David E. Dobbs. "Integrally Closed Condensed Domains are Bézout." Canadian Mathematical Bulletin 28, no. 1 (March 1, 1985): 98–102. http://dx.doi.org/10.4153/cmb-1985-010-x.

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AbstractIt is proved that an integral domain R is a Bézout domain if (and only if) R is integrally closed and I J = {ij|i ∊ I, j ∊ J} for all ideals I and J of R; that is, if (and only if) R is an integrally closed condensed domain. The article then introduces a weakening of the "condensed" concept which, in the context of the k + M construction, is equivalent to a certain field-theoretic condition. Finally, the field extensions satisfying this condition are classified.

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9

Noeske, Felix. "Matching Simple Modules of Condensed Algebras." LMS Journal of Computation and Mathematics 11 (2008): 213–22. http://dx.doi.org/10.1112/s1461157000000577.

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AbstractLet A be a finite dimensional algebra over a finite field F. Condensing an A-module V with two different idempotents e and e′ leads to the problem that to compare the composition series of V e and V e′, we need to match the composition factors of both modules. In other words, given a composition factor S of V e, we have to find a composition factor S′ of V e′ such that there exists a composition factor Ŝ of V with Ŝ e ≅ S and Ŝ e′ ≅ S′, or prove that no such S′ exists. In this note, we present a computationally tractable solution to this problem.

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10

Gottlieb, Christian. "On Condensed Noetherian Domains Whose Integral Closures are Discrete Valuation Rings." Canadian Mathematical Bulletin 32, no. 2 (June 1, 1989): 166–68. http://dx.doi.org/10.4153/cmb-1989-024-7.

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AbstractA condensed domain is an integral domain such that IJ = {xy : x ∊ I, y ∊ J } holds for each pair I, J of ideals. We prove that, under suitable conditions, a subring of a discrete valuation ring is condensed if and only if it contains an element of value 2. We also define the concept strongly condensed.

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11

Awofala, Adeneye Olarewaju, and Oludola Sarah Sopekan. "Early-years future teachers’ mathematical beliefs as determinants of performance in primary mathematics." JRAMathEdu (Journal of Research and Advances in Mathematics Education) 5, no. 1 (February 28, 2020): 54–68. http://dx.doi.org/10.23917/jramathedu.v5i1.9433.

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One construct that lies in between the cognitive and affective domains of mathematics education is belief and this concept is rarely investigated in the Nigerian mathematics education community. Thus, an investigation of early-years future teachers’ mathematical beliefs as determinants of performance in primary mathematics within the blueprint of the quantitative method of the descriptive survey research design was conducted. Three research questions were addressed and secondary data relating to performance in mathematics of 320 early-years future teachers were retrieved from their records at the Department of Arts and Social Sciences Education, University of Lagos, Nigeria. One other instrument labeled Mathematical Beliefs Scale was employed for the collection of key data connected to the mathematical beliefs. The collected data were condensed and explored with the principal components factor analysis, multiple regression analysis, and independent samples t-test. Results showed that mathematical beliefs measured using the Mathematical Beliefs Scale are a multidimensional construct with four-factor structure: emotional and developmental commitment in learning of mathematics; self-assurance and philosophies concerning one's subjective mathematical aptitude; beliefs about mathematics; and mathematical problem-solving beliefs. These factors show adequate and excellent reliabilities as computed using Cronbach alpha. Also, gender was not a factor in early-years future teachers' mathematical beliefs even at the subscale level and the four factors of the mathematical belief scale predicted early-years future teachers' performance in primary mathematics. In line with these results, it is recommended that early-years future teachers be taught in a constructivist manner so that they can imbibe constructivist beliefs capable of engendering better learning of mathematics.

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12

Alfeld, Peter, Larry L. Schumaker, and Tatyana Sorokina. "Two condensed macro-elements with full approximation power." Advances in Computational Mathematics 32, no. 4 (December 13, 2008): 381–91. http://dx.doi.org/10.1007/s10444-008-9110-7.

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13

Gu, Chao, and Guorong Wang. "Condensed cramer rule for solving restricted matrix equations." Applied Mathematics and Computation 183, no. 1 (December 2006): 301–6. http://dx.doi.org/10.1016/j.amc.2006.05.059.

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14

Fan, Jun, and Feng Zhong Sun. "Analysis on Chilled Water Spraying through Extraction Opening in Condenser to Enhance Extraction Effect of Vacuum Pump." Advanced Materials Research 860-863 (December 2013): 737–41. http://dx.doi.org/10.4028/www.scientific.net/amr.860-863.737.

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Non condensable gas (air) accumulating in the condenser will reduce heat transfer coefficient of condense and vacuum value, Reducing of condenser vacuum value will lower turbine efficiency. Chilled water spraying is adopted to cool down the steam before it is extracted through extraction opening in condenser so as to enhance extraction effect of vacuum pump. This paper gives analysis on chilled water spraying through extraction opening. Mathematic model of selected controlling volume near extraction opening is given. Maximum amount of spraying and its relationship with vacuum value and increment of extraction rate are also proposed.

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15

Orlov, A. I. "System fuzzy interval mathematics: the basis of tools of mathematical research methods." Industrial laboratory. Diagnostics of materials 88, no. 7 (July 21, 2022): 5–7. http://dx.doi.org/10.26896/1028-6861-2022-88-7-5-7.

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16

Garbey, Marc, Hans G. Kaper, Gary K. Leaf, and Bernard J. Matkowsky. "Nonlinear analysis of condensed-phase surface combustion." European Journal of Applied Mathematics 1, no. 1 (March 1990): 73–89. http://dx.doi.org/10.1017/s0956792500000061.

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This article is concerned with the structure and stability properties of a combustion front that propagates in the axial direction along the surface of a cylindrical solid fuel element. The fuel consists of a mixture of two finely ground metallic powders, which combine upon ignition in a one-step chemical reaction. The reaction is accompanied by a melting process, which in turn enhances the reaction rate. The combustion products are in the solid state. The reaction zone, inside which the melting occurs, is modelled as a front that propagates along the surface of the cylinder. The different modes of propagation that have been observed experimentally (such as single- and multiheaded spin combustion and multiple-point combustion) are explained as the results of bifurcations from a uniformly propagating plane circular front. The stability properties of the various modes are discussed.

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17

Volpert, Vit A., and Vl A. Volpert. "Propagation Velocity Estimation for Condensed Phase Combustion." SIAM Journal on Applied Mathematics 51, no. 4 (August 1991): 1074–89. http://dx.doi.org/10.1137/0151054.

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18

Volpert, Vit A., Vl A. Volpert, S. P. Davtyan, I. N. Megrabova, and N. F. Surkov. "Two-Dimensional Combustion Modes in Condensed Flow." SIAM Journal on Applied Mathematics 52, no. 2 (April 1992): 368–83. http://dx.doi.org/10.1137/0152020.

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19

Maupin, Sue. "Middle-Grades Geometry Activities." Mathematics Teaching in the Middle School 1, no. 10 (May 1996): 790–96. http://dx.doi.org/10.5951/mtms.1.10.0790.

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Several years ago, when illinois issued its manuals describing the state's learning objectives in mathematics, one school district spent several months examining the mathematics curriculum from kindergarten through the twelfth grade. District goals were written by a committee, condensed to state goals, and submitted to the state as a learning-assessment plan. In the process, deficiencies in the district's curriculum were uncovered. A main deficiency concerned the amount and type of geometry taught in the middle grades.

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20

Donaldson, S. K. "Book Review: Topology of gauge fields and condensed matter." Bulletin of the American Mathematical Society 32, no. 2 (April 1, 1995): 248–52. http://dx.doi.org/10.1090/s0273-0979-1995-00574-4.

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21

Senechal, Marjorie. "Delaunay sets and condensed matter: The dialogue continues." Proceedings of the Steklov Institute of Mathematics 288, no. 1 (January 2015): 259–64. http://dx.doi.org/10.1134/s0081543815010204.

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22

Ghasemi Kamalvand, M., and Kh D. Ikramov. "Reachability of condensed forms via unitary congruence transformations." Computational Mathematics and Mathematical Physics 48, no. 8 (August 2008): 1261–65. http://dx.doi.org/10.1134/s0965542508080010.

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23

Bayliss, A., and B. J. Matkowsky. "Two Routes to Chaos in Condensed Phase Combustion." SIAM Journal on Applied Mathematics 50, no. 2 (April 1990): 437–59. http://dx.doi.org/10.1137/0150026.

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24

Abdalbaqi, Luma S., Luay A. Al-Swidi, and Mustafa Hasan Hadi. "On condensed set in ideal topological spaces." Journal of Interdisciplinary Mathematics 25, no. 5 (July 4, 2022): 1445–51. http://dx.doi.org/10.1080/09720502.2022.2046341.

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25

Rodrigues Jacinto, Joaquín, and Juan Rodríguez Camargo. "Solid locally analytic representations of 𝑝-adic Lie groups." Representation Theory of the American Mathematical Society 26, no. 31 (August 31, 2022): 962–1024. http://dx.doi.org/10.1090/ert/615.

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We develop the theory of locally analytic representations of compact p p -adic Lie groups from the perspective of the theory of condensed mathematics of Clausen and Scholze. As an application, we generalise Lazard’s isomorphisms between continuous, locally analytic and Lie algebra cohomology to solid representations. We also prove a comparison result between the group cohomology of a solid representation and of its analytic vectors.

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26

Russo, Luís M. S., and Arlindo L. Oliveira. "Efficient generation of super condensed neighborhoods." Journal of Discrete Algorithms 5, no. 3 (September 2007): 501–13. http://dx.doi.org/10.1016/j.jda.2006.10.005.

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27

Camerini, Paolo M., and Horst W. Hamacher. "Intersection of Two Matroids: (Condensed) Border Graphs and Ranking." SIAM Journal on Discrete Mathematics 2, no. 1 (February 1989): 16–27. http://dx.doi.org/10.1137/0402002.

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28

Logak, Elisabeth, and Vincent Loubeau. "Travelling wave solutions to a condensed phase combustion model." Asymptotic Analysis 12, no. 4 (1996): 259–94. http://dx.doi.org/10.3233/asy-1996-12401.

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29

LOGAN, J. DAVID, and EDWIN L. WOERNER. "Sensitivity of Self-similar ZND Waves in Condensed Media." IMA Journal of Applied Mathematics 43, no. 2 (1989): 167–84. http://dx.doi.org/10.1093/imamat/43.2.167.

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30

Sharpe, G. J., V. Gorchkov, and M. Short. "Shock initiation of explosives: the idealized condensed-phase model." IMA Journal of Applied Mathematics 73, no. 2 (December 6, 2007): 361–73. http://dx.doi.org/10.1093/imamat/hxm065.

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31

Bolshakova, E. I. "The model for sweetened condensed milk storage under critical temperature conditions." DAIRY INDUSTRY, no. 4 (2023): 42–44. http://dx.doi.org/10.31515/1019-8946-2023-04-42-44.

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32

Kibble, T. W. B., and G. R. Pickett. "Introduction. Cosmology meets condensed matter." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 366, no. 1877 (June 5, 2008): 2793–802. http://dx.doi.org/10.1098/rsta.2008.0098.

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At first sight, low-temperature condensed-matter physics and early Universe cosmology seem worlds apart. Yet, in the last few years a remarkable synergy has developed between the two. It has emerged that, in terms of their mathematical description, there are surprisingly close parallels between them. This interplay has been the subject of a very successful European Science Foundation (ESF) programme entitled COSLAB (‘Cosmology in the Laboratory’) that ran from 2001 to 2006, itself built on an earlier ESF network called TOPDEF (‘Topological Defects: Non-equilibrium Field Theory in Particle Physics, Condensed Matter and Cosmology’). The articles presented in this issue of Philosophical Transactions A are based on talks given at the Royal Society Discussion Meeting ‘Cosmology meets condensed matter’, held on 28 and 29 January 2008. Many of the speakers had participated earlier in the COSLAB programme, but the strength of the field is illustrated by the presence also of quite a few new participants.

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33

Angiulli, Fabrizio. "Condensed Nearest Neighbor Data Domain Description." IEEE Transactions on Pattern Analysis and Machine Intelligence 29, no. 10 (October 2007): 1746–58. http://dx.doi.org/10.1109/tpami.2007.1086.

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34

Booty, Michael R., Stephen B. Margolis, and Bernard J. Matkowsky. "Interaction of Pulsating and Spinning Waves in Condensed Phase Combustion." SIAM Journal on Applied Mathematics 46, no. 5 (October 1986): 801–43. http://dx.doi.org/10.1137/0146050.

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35

Ikramov, Kh D. "Reducing complex matrices to condensed forms by unitary congruence transformations." Mathematical Notes 82, no. 3-4 (October 2007): 492–500. http://dx.doi.org/10.1134/s0001434607090258.

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36

BISI, F., E. C. GARTLAND, and E. G. VIRGA. "A criterion for symmetric tricritical points in condensed ordered phases." European Journal of Applied Mathematics 23, no. 1 (January 5, 2011): 3–28. http://dx.doi.org/10.1017/s0956792510000355.

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Basic methods from bifurcation theory are applied to derive a criterion that predicts when a symmetric tricritical point may occur in a transition between condensed ordered phases described by any finite number of scalar order parameters. At such a point, a change of order takes place in the phase transition, which passes from first to second order, or vice versa.

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Chen, Y., Y. He, and K. P. Shum. "Projectively condensed semigroups, generalized completely regular semigroups and projective orthomonoids." Acta Mathematica Hungarica 119, no. 3 (January 19, 2008): 281–305. http://dx.doi.org/10.1007/s10474-007-7038-x.

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38

Primicerio, Mario, Weiqing Xie, and Muzeng Shu. "On a problem in condensed two-phase combustion." Mathematical Methods in the Applied Sciences 12, no. 6 (June 1990): 519–31. http://dx.doi.org/10.1002/mma.1670120606.

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39

Rediske, Arthur. "The Trisection of an Arbitrary Angle: A Condensed Classical Geometric Solution." JOURNAL OF ADVANCES IN MATHEMATICS 17 (December 10, 2019): 378–89. http://dx.doi.org/10.24297/jam.v17i0.8487.

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This paper presents a short version of an elegant geometric solution of angle trisection that was published by this author on 2018-04-30 in Volume: 14 Issue: 02 of the Journal of Advances in Mathematics. The style of writing for the above paper was based on how teaching geometry was taught in high schools from 1940 to 1942. Proofs of a problem consisted of a statement that was followed by a valid reason why the statement was made. If the proof was many lines in length, the teacher wanted the students to show each step. The students were not allowed to skip a step or steps to reach the final line of the proof. This short version was generated when a copy of the above paper was reviewed by a retired school teacher, who suggested the proof of the trisection of an arbitrary angle could be shortened. The exposed methods of proof have not changed from the Euclidean postulates of classical geometry.

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Lai, Ru-Yu, Ravi Shankar, Daniel Spirn, and Gunther Uhlmann. "An inverse problem from condensed matter physics." Inverse Problems 33, no. 11 (October 26, 2017): 115011. http://dx.doi.org/10.1088/1361-6420/aa8e81.

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41

Kalchev, Delyan Z., and Panayot Vassilevski. "A Condensed Constrained Nonconforming Mortar-Based Approach for Preconditioning Finite Element Discretization Problems." SIAM Journal on Scientific Computing 42, no. 5 (January 2020): A3136—A3156. http://dx.doi.org/10.1137/19m1305690.

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42

d'ALMEIDA, AMAH, and RENÉE GATIGNOL. "THE HALF-SPACE PROBLEM IN DISCRETE KINETIC THEORY." Mathematical Models and Methods in Applied Sciences 13, no. 01 (January 2003): 99–119. http://dx.doi.org/10.1142/s0218202503002404.

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This paper deals with the analysis of the steady flow of a semi-infinite expanse of rarefied gas bounded by its plane condensed phase by the methods of the discrete kinetic theory. The existence of the solutions of the corresponding boundary value problem is discussed. The relations among the parameters of the flow near the condensed phase and at infinity required for the existence of solutions are established. The problem of condensation of a vapor gas on its own condensed phase is then solved analytically for a particular discrete model and remarkable features of the flow are analyzed.

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Кручинин, А. Г., Е. И. Большакова, С. Н. Туровская, and Е. Е. Илларионова. "Study of temperature transitions in sweetened condensed milk under critical storage conditions." Food processing industry, no. 10 (October 4, 2023): 62–65. http://dx.doi.org/10.52653/ppi.2023.10.10.013.

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Транспортирование является частью процесса хранения, и его условия должны обеспечивать сохранность качества продукта при доставке в различные регионы страны. При этом специальные технические возможности для поддержания стабильной температуры в логистическом транспорте на протяжении всего пути являются дорогостоящими, что останавливает многих производителей от расширения территории реализации продукции. На сегодняшний день для сгущенного молока с сахаром представлены новые рекомендуемые пролонгированные сроки годности при различных температурно-влажностных условиях хранения, которые также предусматривают режимы, включающие отрицательные температуры. Однако рекомендации, учитывающие возможные особенности транспортирования данной продукции в районы Крайнего севера или регионы с жарким климатом, в обновленной Типовой технологической инструкции по производству молока и сливок сгущенных с сахаром не предложены. В свою очередь, тепловой поток, температурный градиент и скорость процессов охлаждения и нагревания способны влиять на изменения свойств пищевой системы, что обуславливает необходимость получения новых теоретических данных о температурных переходах от окружающей среды к сгущенному молоку с сахаром, упакованному в традиционную потребительскую тару (металлические банки №7). В работе представлены исследования изменения среднеобъемной температуры сгущенного молока с сахаром в потребительской упаковке при разной последовательности теплового воздействия (нагревание-замораживание, замораживание-нагревание). Выявлено, что при охлаждении и нагревании продукта в потребительской упаковке изменение градиента температур на 10 °C приводит к повышению в 3 раза скорости тепловых процессов. Получены критерии кристаллизации влаги при замораживании в образцах сгущенного цельного молока с сахаром, которые отличаются для центральной и периферийной точек системы и изменяются при предварительном нагревании до температуры, оптимальной для растворения кристаллов лактозы. Описанные результаты позволят использовать их при учете и прогнозировании рисков изменения качественных показателей продукции и станут основой для формирования рекомендаций по особенностям транспортирования в различные регионы страны и на экспорт. Transportation is a part of the storage process, and its conditions must ensure the preservation of product quality during delivery to different regions of the country. At the same time, special technical capabilities to maintain a stable temperature in logistic transport throughout the entire journey are expensive, which stops many producers from expanding their sales territory. To date, for sweetened condensed milk new recommended prolonged shelf life under different temperature and humidity conditions of storage are presented, which also provide for regimes that include negative temperatures. However, recommendations that take into account the possible peculiarities of transportation of these products to the Far North or regions with hot climate in the updated TTI for the production of condensed milk and cream with sugar are not proposed. In turn, the heat flux, temperature gradient and speed of cooling and heating processes can affect the changes in the properties of the food system, which makes it necessary to obtain new theoretical data on the temperature transitions from the environment to condensed milk with sugar in metal can No. 7. The paper presents studies of changes in the average volume temperature of sweetened condensed milk in consumer packaging under different sequences of thermal effects (heating-freezing, freezing-heating). It is revealed that at cooling and heating of the product in consumer package the change of temperature gradient by 10 °C leads to increase in 3 times of thermal processes velocities. The criteria of moisture crystallization during freezing in samples of sweetened condensed whole milk packed in metal can No. 7 have been obtained, which differ for the central and peripheral points of the system and change during preheating to the temperature optimal for dissolution of lactose crystals. The described results will make it possible to use them in accounting and forecasting the risks of changes in the quality indicators of products and will become the basis for the formation of recommendations on the peculiarities of transportation in different regions of the country.

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Cartwright, Julyan H. E. "Nonlinear dynamics determines the thermodynamic instability of condensed matter in vacuo." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2174 (June 8, 2020): 20190534. http://dx.doi.org/10.1098/rsta.2019.0534.

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Abstract:

Condensed matter is thermodynamically unstable in a vacuum. That is what thermodynamics tells us through the relation showing that condensed matter at temperatures above absolute zero always has non-zero vapour pressure. This instability implies that at low temperatures energy must not be distributed equally among atoms in the crystal lattice but must be concentrated. In dynamical systems such concentrations of energy in localized excitations are well known in the form of discrete breathers, solitons and related nonlinear phenomena. It follows that to satisfy thermodynamics such localized excitations must exist in systems of condensed matter at arbitrarily low temperature and as such the nonlinear dynamics of condensed matter is crucial for its thermodynamics. This article is part of the theme issue ‘Stokes at 200 (Part 1)’.

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Maslov, V. P., and O. Yu Shvedov. "The number of bose-condensed particles in a weakly nonideal bose gas." Mathematical Notes 61, no. 5 (May 1997): 661–64. http://dx.doi.org/10.1007/bf02355089.

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Tsarev, S. P. "The Hamilton property of stationary and inverse equations of condensed matter mechanics and mathematical physics." Mathematical Notes of the Academy of Sciences of the USSR 46, no. 1 (July 1989): 569–73. http://dx.doi.org/10.1007/bf01159109.

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Kalinina, E. D., Yu B. Gerber, E. Yu Bogodist-Timofeeva, A. V. Gavrilov, and V. I. Omelchuk. "Study of the effective viscosity of whole hydrolyzed (low-lactose) condensed milk with sugar." DAIRY INDUSTRY, no. 6 (2022): 30–32. http://dx.doi.org/10.31515/1019-8946-2022-06-30-32.

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Ainsworth, Mark, and Charles Parker. "Statically Condensed Iterated Penalty Method for High Order Finite Element Discretizations of Incompressible Flow." SIAM Journal on Scientific Computing 45, no. 6 (December 14, 2023): A3095—A3120. http://dx.doi.org/10.1137/22m1541368.

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Rabinowitz, M., Y. E. Kim, and J. H. Yoon. "Condensed matter effects in the solar neutrino problem." International Journal of Theoretical Physics 33, no. 11 (November 1994): 2189–98. http://dx.doi.org/10.1007/bf00675800.

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Girolami, M., and Chao He. "Probability density estimation from optimally condensed data samples." IEEE Transactions on Pattern Analysis and Machine Intelligence 25, no. 10 (October 2003): 1253–64. http://dx.doi.org/10.1109/tpami.2003.1233899.

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