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Constant amplitude zero auto-correlation (CAZAC) sequences are widely applied in waveforms for radar and communication systems. Motivated by a recent work [Berggren and Popovi\'c, IEEE Trans. Inf. Theory 70(8), 6068-6075 (2024)], this paper…
Constant amplitude zero autocorrelation (CAZAC) sequences have modulus one and ideal periodic autocorrelation function. Such sequences are used in cellular radio communications systems, e.g., for reference signals, synchronization signals…
Quadratic permutation polynomials (QPPs) have been widely studied and used as interleavers in turbo codes. However, less attention has been given to cubic permutation polynomials (CPPs). This paper proves a theorem which states sufficient…
In this paper we study the normalized solutions of the following critical growth Choquard equation with mixed local and non-local operators: \begin{equation*} \begin{array}{rcl} -\Delta_p u +(-\Delta_p)^s u & = & \lambda |u|^{p-2}u +\mu…
In this work, in the context of Linear and Quadratic Programming, we interpret Primal Dual Regularized Interior Point Methods (PDR-IPMs) in the framework of the Proximal Point Method. The resulting Proximal Stabilized IPM (PS-IPM) is…
The predictive power of perturbative QCD (pQCD) depends on two important issues: (1) how to eliminate the renormalization scheme-and-scale ambiguities at fixed order, and (2) how to reliably estimate the contributions of unknown…
We formulate a parity-mixed coupled-cluster (PM-CC) approach for high-precision calculations of parity non-conserving amplitudes in mono-valent atoms. Compared to the conventional formalism which uses parity-proper (PP) one-electron…
We analyse the top-quark decay at the next-to-next-to-leading order (NNLO) in QCD by using the Principle of Maximum Conformality (PMC) which provides a systematic way to eliminate renormalization scheme and scale ambiguities in perturbative…
We present in detail a new systematic method which can be used to automatically eliminate the renormalization scheme and scale ambiguities in perturbative QCD predictions at all orders. We show that all of the nonconformal \beta-dependent…
We have further developed and extended a method for calculation of atomic properties based on a combination of the configuration interaction and coupled-cluster approach. We have applied this approach to the calculation of different…
In this paper, we construct a special family of cyclic codes, known as quadratic residue codes of prime length \( p \equiv \pm 1 \pmod{44} ,\) \( p \equiv \pm 5 \pmod{44} ,\) \( p \equiv \pm 7 \pmod{44} ,\) \( p \equiv \pm 9 \pmod{44} \)…
The well-known Chowla and Zassenhaus conjecture, proven by Cohen in 1990, states that if $p>(d^2-3d+4)^2$, then there is no complete mapping polynomial $f$ in $\Fp[x]$ of degree $d\ge 2$. For arbitrary finite fields $\Fq$, a similar…
Let p be a prime number, and let f, g, and h be three modular forms of weights $\kappa$, $\lambda$, and $\mu$ for $SL(2,\Bbb{Z})$. We suppose $\kappa \geq \lambda + \mu$. In joint work with Kudla, one of the authors obtained a formula for…
Cohn and Kumar showed that the permutation on the set of the classes of left associated Hurwitz primes above an odd prime $p$ induced through metacommutation by a Hurwitz prime $\xi$ of norm $q$ has either $0$, $1$ or $2$ fixed points, and…
In this paper we study the normalized solutions of the following critical growth Choquard equation with mixed local and non-local operators: \begin{equation*} \begin{array}{rcl} -\Delta u +(-\Delta)^s u & = & \lambda u +\mu |u|^{p-2}u…
Let $p=2n+1$ be an odd prime, and let $\zeta_{p^2-1}$ be a primitive $(p^2-1)$-th root of unity in the algebraic closure $\overline{\mathbb{Q}_p}$ of $\mathbb{Q}_p$. We let $g\in\mathbb{Z}_p[\zeta_{p^2-1}]$ be a primitive root modulo…
Mathematical programs with complementarity constraints (MPCCs) are a challenging class of nonlinear optimization problems, because their nonlinear programming reformulations violate standard constraint qualifications at every feasible…
We introduce simple quadrature rules for the family of nonparametric nonconforming quadrilateral element with four degrees of freedom. Our quadrature rules are motivated by the work of Meng {\it et al.} \cite{meng2018new}. First, we…
We analyze two sets of specific functions, that/which form the basis of the nonpower asymptotic expansions both in the timelike and spacelike regions for single scale dependent QCD observables in the Shirkov--Solovtsov's Analytic…
The Cauchy problem for the generalized Zakharov-Kuznetsov equation $$\partial_t u +\partial_x\Delta u=\partial_x u^{k+1}, \qquad \qquad u(0)=u_0$$ is considered in space dimensions $n=2$ and $n=3$ for integer exponents $k \ge 3$. For data…