?
An efficient algorithm for the eigenvalue problem of a Hermitian quaternion matrix in quantum chemistry
Journal of Computational and Applied Mathematics. 2025. Vol. 463.
Guo Z., Jiang T., Wang G., Васильев В. И.
The introduction of quaternions in the quantum chemistry framework provides new ideas for solving some of the difficulties encountered in traditional approaches and is expected to expand the scope of quantum chemistry research. This paper investigates the eigenvalue problem of a Hermitian quaternion matrix by means of the complex representation of a quaternion matrix. This paper also gives an efficient algebraic algorithm for finding the eigenvalues and eigenvectors of a Hermitian quaternion matrix, which requires much less computational time than existing algorithms. This novel algorithm provides an algebraic method for quantum chemistry research and is expected to have potential applications in large-scale molecular structure prediction and reaction mechanism studies.
Keywords: efficient algorithmquantum chemistryeigenvalue problemHermitian quaternion matrixcomplex representation
Publication based on the results of:
Basalaev A., Rarovskii A., Journal of Singularities 2026 Vol. 30 P. 61–80
Saito theory associates to an isolated singularity rich structure that plays an important role in mirror symmetry. In this note we construct Saito theory for A and D type Landau-Ginzburg orbifolds. Namely, for the pairs (f,G), where f defines an isolated singularity of A and D type and G is a group of symmetries of ...
Added: September 1, 2026
Rybakov M., Shkatov D., Journal of Logic and Computation 2026 Vol. 36 No. 6 Article exag026
We prove Pi-1-1-hardness, and thus lack of recursive axiomatizability, of constant-domain modal predicate logics defined by a class of Dedekind complete linear Kripke frames containing a frame with an infinitely increasing chain of worlds. The result holds even for the language with one unary predicate letter, one propositional letter, and two individual variables. ...
Added: September 1, 2026
Селянин Ф. И., Moscow Mathematical Journal 2026 Vol. 26 No. 2 P. 167–187
Minkowski mixed volume of n subpolytopes D1,…,Dn of a polytope P⊂Rn clearly does not exceed the normalized volume n!Vol(P). Equality holds if and only if the subpolytopes are interlaced, i.e., each proper face F⊊P intersects at least dim(F)+1 of the polytopes Di. Efficiently computing mixed volumes for more general collections of subpolytopes is crucial for estimating the complexity of numerically solving polynomial systems.
Motivated by relaxing the bound dim(F)+1 to dim(F), we ...
Added: August 31, 2026
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., International Mathematics Research Notices 2026 Vol. 14 Article rnag146
We prove a recent conjecture of the fourth named author with P. Norbury that states a system of universal polynomial relations among the kappa classes on the moduli spaces of algebraic curves. The proof involves localization and materialization analysis of the spin Gromov–Witten theory of the projective line and is dictated by Z 2 -equivariant ...
Added: August 31, 2026
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., Communications in Mathematical Physics 2026 Vol. 407 No. 69
We prove that for any initial data on a genus zero spectral curve the cor responding correlation differentials of topological recursion are KP integrable. As an application we prove KP integrability of partition functions associated via ELSV-type formulas to the r-th roots of the twisted powers of the log canonical bundles ...
Added: August 31, 2026
Gromov V., Переслегин С. Б., Переслегина Е. Б. et al., СПб.: Полакс, 2026.
Механизм происходящих в мире изменений носит эволюционный, а не экологический характер. Иначе говоря, Человечество столкнулось с кризисом развития, который имеет три независимые составляющие: кризис индустриального общества (фазовый кризис), кризис научного мышления (эпистемный кризис) и кризис формата существования разума (социосистемный кризис). Доклад посвящён аспектам этого триединого кризиса и возможным путям его преодоления, не сводящимся к первичному ...
Added: August 31, 2026
Devyatov R. A., Mathematical notes 2026 Vol. 119 No. 3 P. 782–786
Let G/B be a flag variety over ℂ, where G is a simple algebraic group with a simply laced Dynkin diagram, and B is a Borel subgroup. We say that the product of classes of Schubert divisors in the Chow ring is multiplicity free if it is possible to multiply it by a Schubert class ...
Added: August 30, 2026
Bayer A., Kuznetsov A., Macrì E., Journal fuer die reine und angewandte Mathematik 2026 Vol. 2026 No. 836 P. 111–162
We give a self-contained and simplified proof of Mukai’s classification of prime Fano threefolds of index 1 and genus g ≥ 6 with at most factorial terminal singularities, and of its extension to higher dimension. ...
Added: August 30, 2026
Bayer A., Kuznetsov A., Macrì E., Compositio Mathematica 2026 Vol. 162 No. 1 P. 59–99
We give a proof of Mukai’s theorem on the existence of certain exceptional vector bundles on prime Fano threefolds. To our knowledge this is the first complete proof in the literature. The result is essential for Mukai’s biregular classification of prime Fano threefolds, and for the existence of semiorthogonal decompositions in their derived categories. Our ...
Added: August 30, 2026
Guseva L., Novikov A., Advances in Mathematics 2026 Vol. 503 Article 111211
We prove that the Kuznetsov–Polishchuk exceptional collections on rational homogeneous spaces of the symplectic groups Sp(2n,C) are full and consist of vector bundles. To achieve this, we construct several classes of complexes, which we call generalized staircase complexes, symplectic staircase complexes and secondary staircase complexes — each of which may be of independent interest. ...
Added: August 30, 2026
Polishchuk A., Rains E., Journal of the Institute of Mathematics of Jussieu 2026 Vol. 25 No. 1 P. 339–373
We prove that for every relatively prime pair of integers (d,r) with r>0, there exists an exceptional pair (O,V) on any del Pezzo surface of degree 4, such that V is a bundle of rank r and degree d. As an application, we prove that every Feigin-Odesskii Poisson bracket on a projective space can be ...
Added: August 30, 2026
Kazhdan D., Polishchuk A., Pure and Applied Mathematics Quarterly 2026 Vol. 22 No. 3 P. 1115–1166
We continue the study of automorphic functions associated with a curve C over the ring k[ε]/(ε²), where k is a finite field, begun in arXiv:2303.16259. Namely, we study an example of theta-lifting in this framework and show that it can be understood in terms of the orbit decomposition of the space of automorphic functions S(SL₂(F)\SL₂(A_C)) ...
Added: August 30, 2026
Kuznetsov A. P., Sataev I. R., Stankevich N., Chaos 2026 Vol. 36 No. 8 Article 083131
A radio-physical system, namely, a two-mode van der Pol generator, is considered. It is shown that this system demonstrates two types of chaos: with one and two zero Lyapunov exponents. The regions of the second type of chaos are surrounded by bifurcation lines of invariant tori doubling. Quasi-periodic structures of various shapes are embedded within ...
Added: August 30, 2026
Shirokov N. A., Rozenblum G., Israel Journal of Mathematics 2026 P. 1–30
We establish that a generalized H\¨older continuous function on an (m−2)-Ahlfors regular compact set in Rm can be approximated by solutions of an elliptic equation, with the rate of approximation determined by the continuity modulus of the function ...
Added: August 29, 2026
Avdoshin S.M., Patrushev K. A., Proceedings of the Institute for System Programming of the RAS 2026 No. 4 часть 2 P. 245–256
The cardinality-constrained Markowitz problem is NP-hard and traditionally solved with commercial MIQP solvers. Following the 2022 export restrictions that rendered both commercial MIQP software and cloud quantum platforms (IBM Quantum, D-Wave Leap) inaccessible from the Russian Federation, practitioners require open-source alternatives. This paper systematically compares three solver families for the discrete mean-variance problem: two open-source ...
Added: August 27, 2026
Zaikin A., Vlasenko D., Zakharov D. et al., Diagnostics 2026 Vol. 16 No. 17 P. 1–15
Background/Objectives: Synolitic graphs (SGs) were developed for task-based fMRI, where
edge weights encode the discriminative power of pairwise regional features; whether similar
information can be recovered from resting-state data was untested. We benchmarked
SGs for autism spectrum disorder (ASD) classification using the multisite ABIDE-I dataset
(871 subjects: 403 subjects with ASD, 468 typical controls; 17 sites; CC200 atlas). Methods:
Using ...
Added: August 27, 2026
Melnikov I., Pelinovsky E., Nonlinear Dynamics 2026 No. 114 Article 934
Pyramidal solitons (solitons with more than two inflection points) of the generalized Korteweg–de Vries (KdV) equation are investigated. Necessary and sufficient conditions for the existence of such structures are presented. Within the framework of the generalized Gardner equation — the simplest model that admits pyramidal solitons as solutions — it is shown that these solutions ...
Added: August 27, 2026
Тула: Тульский государственный педагогический университет им. Л.Н. Толстого, 2025.
Сборник содержит материалы, представленные на XXIV Международной конференции «Алгебра, теория чисел, дискретная геометрия и многомасштабное моделирование: современные проблемы, приложения и проблемы истории», посвящённой 110-летию со дня рождения академика Юрия Владимировича Линника и 110-летию со дня рождения профессора Андрея Борисовича Шидловского и 80-летию со дня рождения профессора Геннадия Ивановича Архипова. Материалы конференции будут полезны научным работникам, ...
Added: August 27, 2026
Nesterenko A., Чирский В. Г., Матвеев В. Ю., Чебышевский сборник 2026 Т. 27 № 2 С. 118–127
The article presents the results of a practical study of the statistical properties of some sequences that are values of functions of a special type. ...
Added: August 26, 2026
Eduard Sopin, Nazarin A., Begishev V. et al., IEEE Transactions on Vehicular Technology 2026 Vol. 75 No. 6 P. 10995–11007
Aimed at rate-greedy applications having extreme requirements for the data rate at the air interface, 5G New Radio (NR) systems may experience problems when the number of user equipment (UE) in the coverage of the cell increases due to limited capacity of the physical downlink control channel (PDCCH).The aim of this study is to explore ...
Added: August 26, 2026
Kaimakov K., Malyshev D., Математические заметки 2025 Т. 117 № 5 С. 672–679
В данной работе рассматривается задача о минимальном остовном дереве (кратко, ЗМОД) на произвольном множестве $n$ точек $d$-мерного пространства в $l_1$-норме. Для этой задачи при каждом фиксированном $d\geq 2$ известен алгоритм сложности $O\big(n\cdot (\log\,n + \log^{r_d}\,n\cdot \log\log\,n)\big)$, где $r_d\in \{0,1,2,4\}$ при $d\in \{2,3,4,5\}$ и $r_d=d$ при $d\geq 6$. Для $d=3$ известно улучшение этого результата до сложности ...
Added: January 18, 2025
Kirill V. Kaymakov, Dmitry S. Malyshev, Optimization Letters 2025 Vol. 19 P. 1441–1454
The tolerance of an element of a combinatorial optimization problem with respect to a given optimal solution is the maximum change, i.e., decrease or increase, of its cost, such that this solution remains optimal. The bottleneck path problem, for given an edge-capacitated graph, a source, and a target, is to find the max-min value of ...
Added: November 5, 2024
I. V. Svitanko, Pivina T. S., Russian Chemical Bulletin 2024 Vol. 73 No. 5 P. 1093–1108
The review gives a retrospective of methods for molecular modeling of the structures, mechanisms of chemical reactions, and properties of organic compounds. The development and advancement of the ideology of preliminary modeling of the structures and formation mechanisms of reaction products in the planning of any synthesis is a relevant task in this fi eld of science. Some ...
Added: June 21, 2024
Yaremenko I., Fomenkov D., Budekhin R. et al., Journal of Organic Chemistry 2024 Vol. 89 No. 8 P. 5699–5714
Four heteroatoms dance in the cascade of four pericyclic reactions initiated by ozonolysis of C═N bonds. Switching from imines to semicarbazones introduces the fifth heteroatom that slows this dance, delays reaching the thermodynamically favorable escape path, and allows efficient interception of carbonyl oxides (Criegee intermediates, CIs) by an external nucleophile. The new three-component reaction of ...
Added: June 3, 2024