Related papers: A log canonical threshold test
Asymptotic mean value properties, their converse and some other related results are considered for solutions to the $m$-dimensional Helmholtz equation (metaharmonic functions) and solutions to its modified counterpart (panharmonic…
We provide a necessary condition that a quantum measurement can be implemented by the class of protocols known as Local Operations and Classical Communication, or LOCC, including when an error is allowed but must vanish in the limit of an…
The paper is dealing with semi-classical asymptotics of a characteristic function for a stochastic process. The main technical tool is provided by the stationary phase method. The extremal range for a stochastic process is defined by limit…
We generalize the work of Jian Song to compute the alpha invariant of any (nef and big) toric line bundle in terms of the associated polytope. We use the analytic version of the computation of the log canonical threshold of monomial ideals…
We determine the asymptotic behavior of the realized power variations, or more generally of sums of a given test function evaluated at the successive increments of a L\'{e}vy process. One can completely elucidate the first order behavior…
Some properties of integral averages of functions on intervals and their asymptotic behavior are investigated. The results are aimed at applications to entire and subharmonic functions.
We show that unary log-analytic functions are polynomially bounded. In the higher dimensional case globally a log-analytic function can have exponential growth. We show that a log-analytic function is polynomially bounded on a definable set…
The theory of asymptotic complexity provides an approach to characterizing the behavior of programs in terms of bounds on the number of computational steps executed or use of computational resources. We describe work using ACL2 to prove…
Generalized Lelong numbers of plurisubharmonic functions with respect to plurisubharmonic weights (due to Demailly) are specified for weights with multicircled asymptotics. Explicit formulas for these values are obtained in terms of the…
In this paper we prove existence and multiplicity results of unbounded critical points for a general class of weakly lower semicontinuous functionals. We will apply a suitable nonsmooth critical point theory.
In the present article, we investigate the univalence property of polyanalytic functions and $\log$-$\alpha$-analytic functions. First, by using a new idea, we prove an improved lemma and the coefficient estimates for bounded polyanalytic…
In the paper, the authors concisely survey and review some functions involving the gamma function and its various ratios, simply state their logarithmically complete monotonicity and related results, and find necessary and sufficient…
The paper considers estimates for the asymptotics of summation functions of bounded multiplicative arithmetic functions. Several assertions on this subject are proved and examples are considered.
In various research areas related to decision making, problems and their solutions frequently rely on certain functions being monotonic. In the case of non-monotonic functions, one would then wish to quantify their lack of monotonicity. In…
Summation arithmetic functions with asymptotically independent terms are studied in the paper, the limit of which is the law of normal distribution. Assertions about the asymptotic behavior of the indicated functions are proved.
The normalization of a quasi-log canonical pair is a quasi-log canonical pair.
A common statistical task lies in showing asymptotic normality of certain statistics. In many of these situations, classical textbook results on weak convergence theory suffice for the problem at hand. However, there are quite some…
We give tight bounds for logarithmic mean. We also give new Frobenius norm inequalities for two positive semidefinite matrices. In addition, we give some matrix inequalities on matrix power mean.
Results involving various mean value properties are reviewed for harmonic, biharmonic and metaharmonic functions. It is also considered how the standard mean value property can be weakened to imply harmonicity and belonging to other classes…
We simplify the proof of some widely used theoretical theorems, extending their applicability, while correcting some erroneous results. We also generalize key results and present new results that contribute to the development of the theory.…