相关论文: Correcting a minor error in Cantor's calculation o…
A careful study of the classical/quantum connection with the aid of coherent states offers new insights into various technical problems. This analysis includes both canonical as well as closely related affine quantization procedures. The…
A canonical formulation of effective equations describes quantum corrections by the back-reaction of moments on the dynamics of expectation values of a state. As a first step toward an extension to quantum-field theory, these methods are…
Cantor's famous proof of the non-denumerability of real numbers does apply to any infinite set. The set of exclusively all natural numbers does not exist. This shows that the concept of countability is not well defined. There remains no…
Quantum counting is the task of determining the dimension of the subspace of states that are accepted by a quantum verifier circuit. It is the quantum analog of counting the number of valid solutions to NP problems -- a problem well-studied…
Upon re-examining Arnold's established lemma for explaining his famous limit problem, we have determined that while the lemma itself is correct, there is a defect in the original geometric proof. In this paper, we prove the correctness of…
The errors that arise in a quantum channel can be corrected perfectly if and only if the channel does not decrease the coherent information of the input state. We show that, if the loss of coherent information is small, then approximate…
The corrections to the current algebra mass formulae for the pseudoscalar mesons are analyzed by means of a simultaneous exansion in powers of the light quark masses and powers of 1/N. A set of mass formulae is derived, including an…
We give an application of our extender based Radin forcing to cardinal arithmetic. Using a preparation forcing and interleaving of Cohen and Levy forcings in the normal Radin sequence we get a model with a power function having a fixed…
We introduce two algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. We show that our log-time algorithm always produce…
A subset of the Cantor cube is null-additive if its algebraic sum with any null set is null. We construct a set of cardinality continuum such that: all continuous images of the set into the Cantor cube are null-additive, it contains a…
We propose a simple estimator that allows to calculate the absolute value of a system's partition function from a finite sampling of its canonical ensemble. The estimator utilizes a volume correction term to compensate the effect that the…
In this paper some generalizations of the sum of powers of natural numbers is considered. In particular, the class of sums whose generating function is the power of the generating function for the classical sums of powers is studying. The…
Most of theoretical physics is based on the mathematics of functions of a real or a complex variable; yet we frequently are drawn to try extending our reach to include quaternions. The non-commutativity of the quaternion algebra poses…
We point out a major flaw in the conformable calculus. We demonstrate why it fails at defining a fractional derivative and where exactly these tempting conformability properties come from.
We examine the subtle differences between two possible frameworks for the calculation of quarkonium production. The differences between the two methods are not a concern when one calculates only to leading order in the relativistic…
Quantum Monte Carlo methods provide in principle an accurate treatment of the many-body problem of the ground and excited states of condensed systems. In practice, however, uncontrolled errors such as those arising from the fixed-node and…
This paper is a corrigendum to the article 'On the ideal theorem for number fields`. The main result of this paper proves to be untrue and is replaced by an estimate of a weighted sum with an improved error term.
Some class of sums which naturally include the sums of powers of integers is considered. A number of conjectures concerning a representation of these sums is made.
The classical limit for generalized partition functions is obtained using coherent states. In this framework it is presented a general procedure to obtain all the corrections to the classical limit. In particular, the first and second order…
Let $Q=(q_n)_{n=1}^\infty$ be a sequence of bases with $q_i\ge 2$. In the case when the $q_i$ are slowly growing and satisfy some additional weak conditions, we provide a construction of a number whose $Q$-Cantor series expansion is both…