Asymptotic Formula for the Spectrum of the Linear Problem Describing Periodic Polymer Flows in the Infinite Channel

2018 ◽  
Keyword(s):  
Asymptotic Formula ◽  
Linear Problem ◽  
Polymer Flows

Composites with invisible inclusions: Eigenvalues of ℝ-linear problem

2016 ◽  
Vol 27 (5) ◽  
pp. 796-806
Author(s):  
V. V. MITYUSHEV
Keyword(s):  
Asymptotic Formula ◽  
Integral Equations ◽  
Linear Problem ◽  
Nodal Domains

A new eigenvalue ℝ-linear problem arisen in the theory of metamaterials and neutral inclusions is reduced to integral equations. The problem is constructively investigated for circular non-overlapping inclusions. An asymptotic formula for eigenvalues is deduced when the radii of inclusions tend to zero. The nodal domains conjecture related to univalent eigenfunctions is posed. Demonstration of the conjecture allows to justify that a set of inclusions can be made neutral by surrounding it with an appropriate coating.

Heavy Tails of Discounted Aggregate Claims in the Continuous-Time Renewal Model

2007 ◽  
Vol 44 (02) ◽  
pp. 285-294 ◽  
Author(s):  
Qihe Tang
Keyword(s):  
Asymptotic Formula ◽  
Continuous Time ◽  
Heavy Tails ◽  
Tail Behavior ◽  
Renewal Model ◽  
Discounted Aggregate Claims ◽  
Aggregate Claims ◽  
Tail Asymptotic

We study the tail behavior of discounted aggregate claims in a continuous-time renewal model. For the case of Pareto-type claims, we establish a tail asymptotic formula, which holds uniformly in time.

Approximation properties of Szász type operators involving Charlier polynomials

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 479-487
Author(s):  
Didem Arı
Keyword(s):  
Asymptotic Formula ◽  
Weighted Space ◽  
Approximation Properties ◽  
Charlier Polynomials

In this paper, we give some approximation properties of Sz?sz type operators involving Charlier polynomials in the polynomial weighted space and we give the quantitative Voronovskaya-type asymptotic formula.

scholarly journals On the least common multiple of random q-integers

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Carlo Sanna
Keyword(s):  
Positive Integer ◽  
Asymptotic Formula ◽  
Probabilistic Model ◽  
Expected Value ◽  
Random Set ◽  
Common Multiple ◽  
Least Common Multiple

AbstractFor every positive integer n and for every $$\alpha \in [0, 1]$$ α ∈ [ 0 , 1 ] , let $${\mathcal {B}}(n, \alpha )$$ B ( n , α ) denote the probabilistic model in which a random set $${\mathcal {A}} \subseteq \{1, \ldots , n\}$$ A ⊆ { 1 , … , n } is constructed by picking independently each element of $$\{1, \ldots , n\}$$ { 1 , … , n } with probability $$\alpha $$ α . Cilleruelo, Rué, Šarka, and Zumalacárregui proved an almost sure asymptotic formula for the logarithm of the least common multiple of the elements of $${\mathcal {A}}$$ A .Let q be an indeterminate and let $$[k]_q := 1 + q + q^2 + \cdots + q^{k-1} \in {\mathbb {Z}}[q]$$ [ k ] q : = 1 + q + q 2 + ⋯ + q k - 1 ∈ Z [ q ] be the q-analog of the positive integer k. We determine the expected value and the variance of $$X := \deg {\text {lcm}}\!\big ([{\mathcal {A}}]_q\big )$$ X : = deg lcm ( [ A ] q ) , where $$[{\mathcal {A}}]_q := \big \{[k]_q : k \in {\mathcal {A}}\big \}$$ [ A ] q : = { [ k ] q : k ∈ A } . Then we prove an almost sure asymptotic formula for X, which is a q-analog of the result of Cilleruelo et al.

scholarly journals On the Number of Quadratic Twists with a Rational Point of Almost Minimal Height

2020 ◽  
Author(s):  
Joachim Petit
Keyword(s):  
Asymptotic Formula ◽  
Elliptic Curve ◽  
Asymptotic Estimate ◽  
Rational Point ◽  
Quadratic Fields ◽  
Real Quadratic Fields ◽  
Quadratic Twists ◽  
The Family ◽  
Minimal Height ◽  
Real Quadratic

Abstract We investigate the number of curves having a rational point of almost minimal height in the family of quadratic twists of a given elliptic curve. This problem takes its origin in the work of Hooley, who asked this question in the setting of real quadratic fields. In particular, he showed an asymptotic estimate for the number of such fields with almost minimal fundamental unit. Our main result establishes the analogue asymptotic formula in the setting of quadratic twists of a fixed elliptic curve.

scholarly journals Cooperative Operation Schedules of Energy Storage System and Demand Response Resources Considering Urban Railway Load Characteristic under a Time-of-Use Tariff

2021 ◽  
Vol 16 (3) ◽  
pp. 1273-1284
Author(s):  
Hye Ji Kim ◽  
Hosung Jung ◽  
Young Jun Ko ◽  
Eun Su Chae ◽  
Hyo Jin Kim ◽  
...  
Keyword(s):  
Energy Storage ◽  
Demand Response ◽  
Air Conditioning ◽  
Linear Problem ◽  
Storage System ◽  
Energy Charge ◽  
Energy Storage System ◽  
Peak Reduction ◽  
Railway Stations ◽  
Charging And Discharging Processes

AbstractThis paper proposes an algorithm for the cooperative operation of air conditioning facilities and the energy storage system (ESS) in railway stations to minimize electricity. Unlike traditional load patterns, load patterns of an urban railway station can peak where energy charge rates are not high. Due to this possibility, if applying the traditional peak-reduction algorithm to railway loads, energy changes can increase, resulting in higher electricity bills. Therefore, it is required to develop a new method for minimizing the sum of capacity charges and energy charges, which is a non-linear problem. To get a feasible solution for this problem, we suggest an algorithm that optimizes the facility operation through two optimizations (primary and secondary). This method is applied to the air-quality change model for operating air conditioning facilities as demand-response (DR) resources in railway stations. This algorithm makes it possible to estimate operable DR capacity every hour, rather than calculating the capacity of DR resources conservatively in advance. Finally, we perform a simulation for the application of the proposed method to the operation of DR resources and ESS together. The simulation shows that electricity bills become lowered, and the number of charging and discharging processes of ESS is also reduced.

scholarly journals On Fourier Coefficients of the Symmetric Square L-Function at Piatetski-Shapiro Prime Twins

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1254
Author(s):  
Xue Han ◽  
Xiaofei Yan ◽  
Deyu Zhang
Keyword(s):  
Asymptotic Formula ◽  
Fourier Coefficient ◽  
Cusp Form ◽  
Riemann Hypothesis ◽  
Modular Group ◽  
Fourier Coefficients ◽  
Mean Value ◽  
Symmetric Square ◽  
The Mean ◽  
Almost All

Let Pc(x)={p≤x|p,[pc]areprimes},c∈R+∖N and λsym2f(n) be the n-th Fourier coefficient associated with the symmetric square L-function L(s,sym2f). For any A>0, we prove that the mean value of λsym2f(n) over Pc(x) is ≪xlog−A−2x for almost all c∈ε,(5+3)/8−ε in the sense of Lebesgue measure. Furthermore, it holds for all c∈(0,1) under the Riemann Hypothesis. Furthermore, we obtain that asymptotic formula for λf2(n) over Pc(x) is ∑p,qprimep≤x,q=[pc]λf2(p)=xclog2x(1+o(1)), for almost all c∈ε,(5+3)/8−ε, where λf(n) is the normalized n-th Fourier coefficient associated with a holomorphic cusp form f for the full modular group.

A Contingency Perspective on Effective Prototyping

1993 ◽  
Vol 8 (2) ◽  
pp. 99-109
Author(s):  
Oscar Gutierrez
Keyword(s):  
Project Management ◽  
Problem Solving ◽  
Organizational Support ◽  
Linear Problem ◽  
Systems Development ◽  
Social Mechanism ◽  
Contingency Perspective ◽  
Future Developments ◽  
Product And Process ◽  
Selection Of

Current demands on prototyping emphasize increasingly complex and dynamic applications that require sophisticated social mechanism and process enablers. However, much of the emphasis placed today in systems development under prototyping focuses on the supporting technology. The imbalance between product and process perspectives under this approach is explored. A view of prototyping effectiveness is presented in terms of non-linear problem solving, adequate technical and procedural solutions, and organizational support. Implications of this view are presented on the selection of prototyping techniques and on project management concerns. Future developments in prototyping practice are explored.

XLIX.—Generalizations of a Problem of Pillai

1949 ◽  
Vol 62 (4) ◽  
pp. 460-469
Author(s):  
L. Mirsky
Keyword(s):  
Asymptotic Formula ◽  
Error Term ◽  
Main Concern ◽  
Positive Integers ◽  
Infinite Set

I. Throughout this paper k1, …, k3 will denote s ≥ I fixed distinct positive integers. Some years ago Pillai (1936) found an asymptotic formula, with error term O(x/log x), for the number of positive integers n ≤ x such that n + k1, …, n + k3 are all square-free. I recently considered (Mirsky, 1947) the corresponding problem for r-free integers (i.e. integers not divisible by the rth power of any prime), and was able, in particular, to reduce the error term in Pillai's formula.Our present object is to discuss various generalizations and extensions of Pillai's problem. In all investigations below we shall be concerned with a set A of integers. This is any given, finite or infinite, set of integers greater than 1 and subject to certain additional restrictions which will be stated later. The elements of A will be called a-numbers, and the letter a will be reserved for them. A number which is not divisible by any a-number will be called A-free, and our main concern will be with the study of A-free numbers. Their additive properties have recently been investigated elsewhere (Mirsky, 1948), and some estimates obtained in that investigation will be quoted in the present paper.

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