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multiHIVE: Hierarchical Multimodal Deep Generative Modeling for Single-cell Multiomics

Nanduri A, Pavan MK, Pandey K, Zafar H.
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Approximate nonsymmetric solutions of many-particle equations and some identities for the density matrix

Mathematical Notes, 1996
1. I. I. vorovich, in: Proceedings of H All-Union Congress on Theoretical and Applied Mechanics [in Russian], Vol. 3, Nauka, Moscow (1966), pp. 116-136. 2. V. E. KovaVchuk and I. I. Vorovich, Prikl. Mat. Mekh. [J. Appl. Math. Mech.], 31, No. 5, 861-869 (1967). 3. V. E. Koval~chuk, PriM. Mat. Mekh. [J. Appl. Math. Mech.], as, No. 3, 511-518 (1969).
Maslov, V. P., Shvedov, O. Yu.
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Operator Identities and the Solution of Linear Matrix Difference and Differential Equations

Studies in Applied Mathematics, 1994
We use operator identities in order to solve linear homogeneous matrix difference and differential equations and we obtain several explicit formulas for the exponential and for the powers of a matrix as an example of our methods. Using divided differences we find solutions of some scalar initial value problems and we show how the solution of matrix ...
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On Systems of Integro-Differential and Integral Equations with Identically Singular Matrix Multiplying the Principal Part

Differential Equations, 2022
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Bulatov, M. V., Solovarova, L. S.
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Bessel equation as an operator identity's matrix element in quantum mechanics

Physics Letters A, 2004
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Fan, Hong-Yi, Li, Chao
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On the Centro-symmetric Solution of a System of Matrix Equations over a Regular Ring with Identity

Algebra Colloquium, 2007
In this paper, we find the centro-symmetric solution of a system of matrix equations over an arbitrary regular ring [Formula: see text] with identity. We first derive some necessary and sufficient conditions for the existence and an explicit expression of the general solution of the system of matrix equations A1X1 = C1, A2X1 = C2, A3X2 = C3, A4X2 = C4
Wang, Qingwen, Chang, Haixia, Lin, Chunyan   +2 more
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The number of solutions to the alternate matrix equation over a finite field and a q-identity

Journal of Statistical Planning and Inference, 2001
Let \(F_q\) be a finite field with \(q\) elements, where \(q\) is a power of a prime. In this paper, the authors first correct a counting error for the formula \(N(K_{2\nu}, O^{(m)})\) occurring in a paper by \textit{L. Carlitz} [Arch. Math. 5, 19-31 (1954; Zbl 0056.01702)].
Wei, Hongzeng, Zhang, Yibin
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Equation for Density Matrix Systems of Identical Particles

2020
The equations for the statistical operator and the density matrix are considered here for a single particle and a system of identical particles when dissipative forces act on them. From the equation for the density matrix, a kinetic equation can be obtained when the density matrix is diagonal. These equations are the basis for the study of the simplest
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Matrix Kadomtsev Petviashvili equation: matrix identities and explicit non-singular solutions

Journal of Physics A: Mathematical and General, 2003
Summary: A new version of the Bäcklund--Darboux transformation for the matrix Kadomtsev-Petviashvili (KP) equation is used to construct and study explicit multi-parameter solutions and wavefunctions (in terms of the matrix exponents). A class of the self-adjoint non-singular solutions of KP I is introduced using the controllability notion from system ...
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Equations of motion with the identity mass matrix for holonomic systems

Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2004
Some consequences concerning holonomic systems described in terms of the inertial quasi-velocities (IQV) are discussed in this note. Introducing the IQV vector into Lagrange's formulation leads to first-order equations with the identity mass matrix of the system.
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