相关论文: The Chung-Graham Expansion
Starting from a small number of well-motivated axioms, we derive a unique definition of sums with a noninteger number of addends. These "fractional sums" have properties that generalize well-known classical sum identities in a natural way.…
A new way of orthogonalizing ensembles of vectors by "lifting" them to higher dimensions is introduced. This method can potentially be utilized for solving quantum decision and computing problems.
We derive a general recurrence relation for squares of Fibonacci-like numbers. Various properties are developed, including double binomial summation identites.
In this paper, we answer the question: "what is the qth Fibonacci number, where q is a positive rational?". The answer is the codenominator function, which is an integral-valued map. It is defined via a pair of functional equations. Many…
In our preceding paper, we have proposed an algorithm for obtaining finite-norm solutions of higher-order linear ordinary differential equations of the Fuchsian type [\sum_m p_m (x) (d/dx)^m] f(x) = 0 (where p_m is a polynomial with…
An enormous variety of quantum nanoobjects and nanosystems calls for the development of new approaches to their description and parametrization. Corresponding methods should be simple, universal enough and ensuring the retention of…
In this paper, it is proved that every sufficiently large even integer can be represented as the sum of two squares of primes, two cubes of primes, two biquadrates of primes and 16 powers of 2. Furthermore, there are at least 5.313% odd…
An equivalent definition of the Fibonacci numbers is that they are the unique sequence such that every integer can be written uniquely as a sum of non-adjacent terms. We can view this as we have bins of length 1, we can take at most one…
Let $a$ and $b$ be positive integers with prime factorisations $a = p_1^np_2^n$ and $b = q_1^nq_2^n$. We prove that the number of essentially distinct $\alpha$-graceful labelings of the complete bipartite graph $K_{a, b}$ equals the…
A conjecture of Cai-Zhang-Shen for figurate primes says that every integer $k>1$ is the sum of two figurate primes. In this paper we give an equivalent proposition to the conjecture. By considering extreme value problems with constraints…
In this paper, we establish a q-analog of partial fraction decomposition formula. By using formula, we develop new closed form representations of sums of q-harmonic numbers and reciprocal q-binomial coefficients. Moreover, we give explicit…
A well-known generalisation of positional numeration systems is the case where the base is the residue class of $x$ modulo a given polynomial $f(x)$ with coefficients in (for example) the integers, and where we try to construct finite…
We extend the Chomsky/Sch\"utzenberger method of computing the growth series of an unambiguous context-free language to the larger class of indexed languages. We illustrate the technique with numerous examples.
We introduce a global equivariant refinement of algebraic K-theory; here `global equivariant' refers to simultaneous and compatible actions of all finite groups. Our construction turns a specific kind of categorical input data into a global…
For a hypergraphic polytope there is a weighted quasisymmetric function which enumerates positive integer points in its normal fan and determines its f-polynomial. This quasisymmetric function invariant of hypergraphs extends the Stanley…
Compressed inverted indices in use today are based on the idea of gap compression: documents pointers are stored in increasing order, and the gaps between successive document pointers are stored using suitable codes which represent smaller…
The recursive method for computing the generalized LM-inverse of a constant rectangular matrix augmented by a column vector is proposed in Udwadia and Phohomsiri (2007) [16] and [17]. The corresponding algorithm for the sequential…
Unitary representations of kinematical symmetry groups of quantum systems are fundamental in quantum theory. We propose in this paper its generalization to quantum kinematical groups. Using the method, proposed by us in a recent paper…
We study Schubert polynomials using geometry of infinite-dimensional flag varieties and degeneracy loci. Applications include Graham-positivity of coefficients appearing in equivariant coproduct formulas and expansions of back-stable and…
We introduce a new method of expressing a $k$-graph $C^*$-algebra as a Cuntz-Pimsner algebra. Kumjian, Pask, and Sims have done this directly, using a linking algebra approach and a $(k-1)$-graph algebra. This can be iterated downward. Our…