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Given n samples(viewed as an n-tuple) of a γ-regular discrete distribution π,in this article the authors concern with the weighted and unweighted graphs induced by the n samples. They first prove a series of SLLN results(of Dvoretzky-Erd¨os’ type). Then they show that the vertex weights of the graphs under investigation obey asymptotically power law distributions with exponent 1 + γ. They also give a conjecture that the degrees of unweighted graphs would exhibit asymptotically power law distribu...  相似文献   
5.
We study two types of dynamical extensions of Lucas sequences and give elliptic solutions for them. The first type concerns a level-dependent (or discrete time-dependent) version involving commuting variables. We show that a nice solution for this system is given by elliptic numbers. The second type involves a non-commutative version of Lucas sequences which defines the non-commutative (or abstract) Fibonacci polynomials introduced by Johann Cigler. If the non-commuting variables are specialized to be elliptic-commuting variables the abstract Fibonacci polynomials become non-commutative elliptic Fibonacci polynomials. Some properties we derive for these include their explicit expansion in terms of normalized monomials and a non-commutative elliptic Euler–Cassini identity.  相似文献   
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We investigate a piecewise-deterministic Markov process with a Polish state space, whose deterministic behaviour between random jumps is governed by a finite number of semiflows. We provide tractable conditions ensuring a form of exponential ergodicity and the strong law of large numbers for the chain given by the post-jump locations. Further, we establish a one-to-one correspondence between invariant measures of the chain and those of the continuous-time process. These results enable us to derive the strong law of large numbers for the latter. The studied dynamical system is inspired by certain models of gene expression, which are also discussed here.  相似文献   
7.
Despite the exceptionally high energy density of lithium metal anodes, the practical application of lithium‐metal batteries (LMBs) is still impeded by the instability of the interphase between the lithium metal and the electrolyte. To formulate a functional electrolyte system that can stabilize the lithium‐metal anode, the solvation behavior of the solvent molecules must be understood because the electrochemical properties of a solvent can be heavily influenced by its solvation status. We unambiguously demonstrated the solvation rule for the solid‐electrolyte interphase (SEI) enabler in an electrolyte system. In this study, fluoroethylene carbonate was used as the SEI enabler due to its ability to form a robust SEI on the lithium metal surface, allowing relatively stable LMB cycling. The results revealed that the solvation number of fluoroethylene carbonate must be ≥1 to ensure the formation of a stable SEI in which the sacrificial reduction of the SEI enabler subsequently leads to the stable cycling of LMBs.  相似文献   
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The paper deals with global solutions of Navier‐Stokes equations with infrared‐damped initial data in the context of Haar wavelets and function spaces of type where .  相似文献   
9.
The Turán number ex(n,G) is the maximum number of edges in any n-vertex graph that does not contain a subgraph isomorphic to G. A wheelWn is a graph on n vertices obtained from a Cn?1 by adding one vertex w and making w adjacent to all vertices of the Cn?1. We obtain two exact values for small wheels:
ex(n,W5)=?n24+n2?,
ex(n,W7)=?n24+n2+1?.
Given that ex(n,W6) is already known, this paper completes the spectrum for all wheels up to 7 vertices. In addition, we present the construction which gives us the lower bound ex(n,W2k+1)>?n24?+?n2? in general case.  相似文献   
10.
We present here some results on the applications of linear recursive sequences of order $2$ to the Fermat pseudoprimes, Fibonacci pseudoprimes, and Dickson pseudoprimes.  相似文献   
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