With the work of Khot and Vishnoi [18] as a starting point, we obtain integrality gaps for certain strong SDP relaxations of U G. Specifically, we exhibit a U G gap instance for the basic semidefinite program strengthened by all valid linear inequalities on the inner products of up to exp(Ω(log log n)1/4) vectors. For a stronger relaxation obtained from the basic semidefinite ...

In this research, the protonation constant value of tannic acid was determined at 25 °C and different ionic strengths (0.1 to 0.7 mol/dm3 NaCl) using potentiometric titration technique. The dependence of protonation constant on ionic strength was modeled and discussed by a Debye-Hückel type equation. Then, based on the obtained data from experiments, the minimizing Sum o...

A new family of distributions called the Kumaraswamy Rayleigh is defied and studied. Some its relevant statistical properties are derived. Many bivariate type G families using Farlie-Gumbel-Morgenstern, modified Farlie-Gumbel-Morgenstern copula, Clayton copula Renyi’s entropy The method maximum likelihood estimation used. special models based on log-logistic, exponential, Weibull, Rayleigh, Par...

Introduced by Kraitchik and Lehmer, an x-pseudosquare is a positive integer n ≡ 1 (mod 8) that is a quadratic residue for each odd prime p ≤ x, yet is not a square. We give a subexponential upper bound for the least x-pseudosquare that improves on a bound that is exponential in x due to Schinzel. We also obtain an equi-distribution result for pseudosquares. An x-pseudopower to base g is a posit...

In this paper, an attempt is made to discover the distribution of COVID-19 spread in different countries such as; Saudi Arabia, Italy, Argentina and Angola by specifying optimal statistical for analyzing mortality rate COVID-19. A new generalization recently inverted Topp Leone distribution, called Kumaraswamy Topp–Leone proposed combining Kumaraswamy-G family distribution. We initially provide...

A partition (C1, C2, ..., Cq) ofG = (V,E) into clusters of strong (respectively, weak) diameter d, such that the supergraph obtained by contracting each Ci is l-colorable is called a strong (resp., weak) (d, l)network-decomposition. Network-decompositions were introduced in a seminal paper by Awerbuch, Goldberg, Luby and Plotkin in 1989. Awerbuch et al. showed that strong (exp{O(√logn log logn)...

A k-query locally decodable code (LDC) C : Σn → ΓN encodes each message x into a codeword C(x) such that each symbol of x can be probabilistically recovered by querying only k coordinates of C(x), even after a constant fraction of the coordinates have been corrupted. Yekhanin (2008) constructed a 3-query LDC of subexponential length, N = exp(exp(O(log n/ log log n))), under the assumption that ...