We look for UV fixed points of non-abelian $SU(n_c)$ gauge theories in $4+2\epsilon$ dimensions with $n_f$ Dirac fermions the fundamental representation, using available five-loop $\overline{{\rm MS}}$ $\beta$-function and employing Pad\'e-Borel resummation techniques Pad\'e approximants to series expansion $\epsilon$. find evidence a $5d$ UV-fixed point $SU(2)$ $n_f\leq 4$ pure $n_c\leq 4$. al...

Explicit function forms of hyperelliptic solutions of Korteweg-de Vries (KdV) and Kadomtsev-Petviashvili (KP) equations were constructed for a given curve y = f(x) whose genus is three. This study was based upon the fact that about one hundred years ago (Acta Math. (1903) 27, 135-156), H. F. Baker essentially derived KdV hierarchy and KP equation by using bilinear differential operator D, ident...

This paper deals with the robust filtering problem for a class of regionally stable nonlinear systems subject to uncertain parameters belonging to a given polytope. The nonlinear system is represented by differential-algebraic equations where the system matrices are allowed to be rational functions of the state and uncertain parameters. Linear matrix inequality conditions based on a parameter-d...

We consider linear control systems of the form ẋ(t)=Ax(t)−μBCx(t) where μ is a positive real parameter, A state operator and generates C0−semigroup contractions S(t) on Banach space X, B C are respectively operators observability, which defined in appropriate spaces they unbounded some sense. aim to show exponential stability above system under sufficient conditions expressed terms admissibilit...

ABSTRACT An operator formalism for bosonic β − γ system on arbitrary algebraic curves is introduced. The classical degrees of freedom are identified and their commutation relations are postulated. The explicit realization of the algebra formed by the fields is given in the Hilbert space equipped with a bilinear form. The construction is based on the ”gaussian” representation for β − γ system on...

We obtain new estimates for a class of oscillatory integral operators with folding canonical relations satisfying a curvature condition. The main lower bounds showing sharpness are proved using Kakeya set constructions. As a special case of the upper bounds we deduce optimal L p (S 2) → L q (RS 2) estimates for the Fourier extension operator on large spheres in R 3 , which are uniform in the ra...

The paper deals with the genericity of domain-dependent spectral properties of the Laplacian-Dirichlet operator. In particular we prove that, generically, the squares of the eigenfunctions form a free family. We also show that the spectrum is generically non-resonant. The results are obtained by applying global perturbations of the domains and exploiting analytic perturbation properties. The wo...

The chiral symmetry of QCD is studied at finite temperature and chemical potential using the Schwinger-Dyson equation in the improved ladder approximation. We calculate three order parameters; the vacuum expectation value of the quark bilinear operator, the pion decay constant and the quark mass gap. We have a second order phase transition at the temperature Tc = 169 MeV along the zero chemical...

In this study, the standard IEEE 754–2008 and modulo-based floor functions for rounding non-integers have been presented. Their effects on the accuracy of the bilinear interpolation algorithm have been demonstrated. The improved-floor uses the modulo operator in an effort to make each non-integer addend an integer when the remainder between the multiplicative inverse of the fractional factor an...

Numerical and experimental realizations of quantum control are closely connected to the properties of the mapping from the control to the unitary propagator [14]. For bilinear quantum control problems, no general results are available to fully determine when this mapping is singular or not. In this paper we give sufficient conditions, in terms of elements of the evolution semigroup, for a traje...