On the functional equation $${\varvec{f}}({\varvec{x}})+{\varvec{f}}({\varvec{y}})=\mathbf{max} \{{\varvec{f}}({\varvec{xy}}),{\varvec{f}}({\varvec{xy}}^{-{\varvec{1}}})\}$$f(x)+f(y)=max{f(xy),f(xy-1)} on groups
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DOI: 10.1007/s00013-017-1061-0
Abstract: We analyse the functional equation $$\begin{aligned} f(x)+f(y)=\max \{f(xy),f(xy^{-1})\} \end{aligned}$$f(x)+f(y)=max{f(xy),f(xy-1)}for a function $$f:G\rightarrow \mathbb R$$f:G→R where G is a group. Without further assumption it characterises the absolute value of additive functions. In addition $$\{z\in G\mid f(z)=0\}$${z∈G∣f(z)=0}… read more here.
Keywords: varvec varvec; varvec; functional equation; max ... See more keywords
On the image, characterization, and automatic continuity of $$\varvec{(\sigma }, \varvec{\tau }$$(σ,τ)-derivations
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DOI: 10.1007/s00013-017-1082-8
Abstract: The first main theorem of this paper asserts that any $$(\sigma , \tau )$$(σ,τ)-derivation d, under certain conditions, either is a $$\sigma $$σ-derivation or is a scalar multiple of ($$\sigma - \tau $$σ-τ), i.e. $$d… read more here.
Keywords: tau; varvec; sigma tau; sigma ... See more keywords
Decay rates for the magneto-micropolar system in $$\varvec{L^2(}\pmb {\mathbb {R}}^{\varvec{n)}}$$L2(Rn)
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DOI: 10.1007/s00013-018-1186-9
Abstract: In this paper, the large time decay of the magneto-micropolar fluid equations on $$\mathbb {R}^n$$Rn ($$ n=2,3$$n=2,3) is studied. We show, for Leray global solutions, that $$ \Vert ({\varvec{u}},{\varvec{w}},{\varvec{b}})(\cdot ,t) \Vert _{{L^2(\mathbb {R}^n)}} \rightarrow 0… read more here.
Keywords: micropolar system; varvec; magneto micropolar; rates magneto ... See more keywords
Purely Atomic Representations of Higher-Rank Graph $$\varvec{C}^{\varvec{*}}$$C∗-Algebras
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DOI: 10.1007/s00020-018-2493-z
Abstract: We study purely atomic representations of $$C^*$$C∗-algebras associated to row-finite and source-free higher-rank graphs. We describe when purely atomic representations are unitarily equivalent and we give necessary and sufficient conditions for a purely atomic representation… read more here.
Keywords: atomic representations; representations higher; varvec; higher rank ... See more keywords
On Liouville Type Theorem for Stationary Non-Newtonian Fluid Equations
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DOI: 10.1007/s00332-020-09615-y
Abstract: In this paper, we prove a Liouville type theorem for non-Newtonian fluid equations in $$\mathbb R^3$$ R 3 , having the diffusion term $${\varvec{A}}_p( u)=\nabla \cdot ( |{\varvec{D}}(u)|^{p-2} {\varvec{D}}(u))$$ A p ( u ) =… read more here.
Keywords: varvec; newtonian fluid; type theorem; liouville type ... See more keywords
On the Spin Projection Operator and the Probabilistic Meaning of the Bipartite Correlation Function
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DOI: 10.1007/s10701-019-00313-8
Abstract: Spin is a fundamental and distinctive property of the electron, having far-reaching implications. Yet its purely formal treatment often blurs the physical content and meaning of the spin operator and associated observables. In this work… read more here.
Keywords: varvec; projection operator; spin; spin projection ... See more keywords
Quasi-classical trajectory insight into stereodynamics for reaction $$\hbox {He}+\hbox {D}_{2}^{+}\rightarrow \hbox {HeD}^{+}+\hbox {D}$$He+D2+→HeD++D with the improved potential energy surface
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DOI: 10.1007/s10910-017-0732-1
Abstract: In this work, a theoretical study on the detailed vector correlation for the reaction $$\hbox {He}+\hbox {D}_{2}^{+}\rightarrow \hbox {HeD}^{+}+\hbox {D}~(\hbox {v}, \hbox {j})$$He+D2+→HeD++D(v,j) has been carried out at the collision energy of 23.06 kcal/mol with… read more here.
Keywords: energy; varvec; hbox hbox; hbox hed ... See more keywords
Parametrization of quantum states based on the quantum state discrimination problem
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DOI: 10.1007/s11128-019-2261-2
Abstract: A discrimination problem consists of N linearly independent pure quantum states $$\Phi =\{|\phi _i\rangle \}$$Φ={|ϕi⟩} and the corresponding occurrence probabilities $$\eta =\{\eta _i\}$$η={ηi}. With any such problem, we associate, up to a permutation over the… read more here.
Keywords: varvec; discrimination problem; problem; varvec rho ... See more keywords
Duality for nondifferentiable minimax fractional programming problem involving higher order $$(\varvec{C},\varvec{\alpha}, \varvec{\rho}, \varvec{d})$$(C,α,ρ,d)-convexity
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DOI: 10.1007/s12597-016-0295-0
Abstract: Abstract In this paper, we present new class of higher-order $$(C, \alpha , \rho , d)$$(C,α,ρ,d)-convexity and formulate two types of higher-order duality for a nondifferentiable minimax fractional programming problem. Based on the higher-order $$(C,… read more here.
Keywords: varvec; convexity; higher order; duality nondifferentiable ... See more keywords
The behavior of the Gauss-Radau upper bound of the error norm in CG
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DOI: 10.48550/arxiv.2209.14601
Abstract: Consider the problem of solving systems of linear algebraic equations $$\varvec{A}\varvec{x}=\varvec{b}$$ A x = b with a real symmetric positive definite matrix $$\varvec{A}$$ A using the conjugate gradient (CG) method. To stop the algorithm at… read more here.
Keywords: behavior; error; varvec; upper bound ... See more keywords