Scrambling in hyperbolic black holes: shock waves and pole-skipping
Sign Up to like & getrecommendations! Published in 2019 at "Journal of High Energy Physics"
DOI: 10.1007/jhep10(2019)257
Abstract: A bstractWe study the scrambling properties of (d + 1)-dimensional hyperbolic black holes. Using the eikonal approximation, we calculate out-of-time-order correlators (OTOCs) for a Rindler-AdS geometry with AdS radius ℓ, which is dual to a… read more here.
Keywords: pole skipping; shock waves; black holes; waves pole ... See more keywords
Ground State Solutions for Asymptotically Periodic Kirchhoff-Type Equations with Asymptotically Cubic or Super-cubic Nonlinearities
Sign Up to like & getrecommendations! Published in 2017 at "Mediterranean Journal of Mathematics"
DOI: 10.1007/s00009-017-1010-y
Abstract: This paper is concerned with the following Kirchhoff-type equation $$\begin{aligned} -\left( a+b\int _{\mathbb {R}^3}|\nabla {u}|^2\mathrm {d}x\right) \triangle u+V(x)u=f(x, u), \quad x\in \mathbb {R}^{3}, \end{aligned}$$-a+b∫R3|∇u|2dx▵u+V(x)u=f(x,u),x∈R3,where $$V\in \mathcal {C}(\mathbb {R}^{3}, (0,\infty ))$$V∈C(R3,(0,∞)), $$f\in \mathcal {C}({\mathbb {R}}^{3}\times \mathbb… read more here.
Keywords: tau; asymptotically periodic; frac; mathbb ... See more keywords
Inequalities for trigonometric sums and applications
Sign Up to like & getrecommendations! Published in 2019 at "Aequationes mathematicae"
DOI: 10.1007/s00010-019-00657-6
Abstract: We present various new inequalities for cosine and sine sums. Among others, we prove that 0.1 $$\begin{aligned} 0\le \sum _{k=0}^n \frac{ (a)_{2k}}{(2k)!} \frac{\cos ((2k+1)x)}{2k+1} \quad {(a\in \mathbb {R})} \end{aligned}$$ 0 ≤ ∑ k = 0… read more here.
Keywords: trigonometric sums; sums applications; inequalities trigonometric; frac ... See more keywords
A sharp upper bound for the sum of reciprocals of least common multiples
Sign Up to like & getrecommendations! Published in 2019 at "Acta Mathematica Hungarica"
DOI: 10.1007/s10474-019-00984-9
Abstract: Let $$n$$ n and $$k$$ k be positive integers such that $$n\ge k+1$$ n ≥ k + 1 and let $$\{a_i\}_{i=1}^n$$ { a i } i = 1 n be an arbitrary given strictly increasing… read more here.
Keywords: upper bound; frac; frac rfloor; lfloor frac ... See more keywords
Improved lower bounds on the degree–diameter problem
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Algebraic Combinatorics"
DOI: 10.1007/s10801-018-0822-6
Abstract: Let C(d, k) and AC(d, k) be the largest order of a Cayley graph and a Cayley graph based on an abelian group, respectively, of degree d and diameter k. It is well known that $$C(d,k)\le 1+d+d(d-1)+\cdots… read more here.
Keywords: degree diameter; graph; diameter problem; frac ... See more keywords
Spherical Model on a Cayley Tree: Large Deviations
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Statistical Physics"
DOI: 10.1007/s10955-016-1696-4
Abstract: We study the spherical model of a ferromagnet on a Cayley tree and show that in the case of empty boundary conditions a ferromagnetic phase transition takes place at the critical temperature $$T_\mathrm{c} =\frac{6\sqrt{2}}{5}J$$Tc=625J, where… read more here.
Keywords: temperature; cayley; spherical model; frac ... See more keywords
Singular value inequalities and applications
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DOI: 10.1007/s11117-020-00790-6
Abstract: It is shown among other inequalities that if A, B and X are $$n\times n$$ complex matrices such that A and B are positive semidefinite, then $$s_{j}(AX-XB)\le $$ $$s_{j}\left( \left( \frac{1}{2}A+\frac{1}{2}A^{1/2}\left| X^{*}\right| ^{2}A^{1/2}\right) \oplus \left( \frac{1}{2}B+\frac{1}{2}… read more here.
Keywords: singular value; inequalities applications; right right; value inequalities ... See more keywords
Optimal online algorithms for MapReduce scheduling on two uniform machines
Sign Up to like & getrecommendations! Published in 2019 at "Optimization Letters"
DOI: 10.1007/s11590-018-01384-8
Abstract: We study online scheduling on two uniform machines in the MapReduce system. Each job consists of two sets of tasks, namely the map tasks and reduce tasks. A job’s reduce tasks can only be processed… read more here.
Keywords: preemptive reduce; reduce tasks; two uniform; scheduling two ... See more keywords
A class of constacyclic BCH codes
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DOI: 10.1007/s12095-019-00401-6
Abstract: Constacyclic codes are a subclass of linear codes and have been well studied. Constacyclic BCH codes are a family of constacyclic codes and contain BCH codes as a subclass. Compared with the in-depth study of… read more here.
Keywords: frac; class constacyclic; bch codes; constacyclic bch ... See more keywords
Geochemical cycle of hydraulic fracturing fluids: Implications for fracture functionality and frac job efficiency in tight sandstone
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Petroleum Science and Engineering"
DOI: 10.1016/j.petrol.2021.109596
Abstract: Abstract The efficiency of the hydraulic fracturing processes is measured through its success rate in opening fracture space, fracturing fluid injectivity, and recovery rates of flowback fluid. This paper applies the volumetric ratio (RFF/FW) between… read more here.
Keywords: water; fracturing fluids; fracturing fluid; frac ... See more keywords
QUADRATIC NONRESIDUES AND NONPRIMITIVE ROOTS SATISFYING A COPRIMALITY CONDITION
Sign Up to like & getrecommendations! Published in 2018 at "Bulletin of the Australian Mathematical Society"
DOI: 10.1017/s0004972718001065
Abstract: Let $q\geq 1$ be any integer and let $\unicode[STIX]{x1D716}\in [\frac{1}{11},\frac{1}{2})$ be a given real number. We prove that for all primes $p$ satisfying $$\begin{eqnarray}p\equiv 1\!\!\!\!\hspace{0.6em}({\rm mod}\hspace{0.2em}q),\quad \log \log p>\frac{2\log 6.83}{1-2\unicode[STIX]{x1D716}}\quad \text{and}\quad \frac{\unicode[STIX]{x1D719}(p-1)}{p-1}\leq \frac{1}{2}-\unicode[STIX]{x1D716},\end{eqnarray}$$ there exists… read more here.
Keywords: nonprimitive roots; stix x1d716; frac; nonresidues nonprimitive ... See more keywords