相关论文: New Proofs for Several Properties of Capacities
This short note present a "proof" of $P\neq NP$. The "proof" with double quotation marks is to indicate that we do not know whether the proof is correct or not (We're confused because we do know in which we make the mistakes).
We introduce concept of next generation shape invariance and show that the process of shape invariant extension can be continued indefinitely.
In recent years, there were a number of experimental developments and discoveries of novel superconducting materials which exhibit multicomponent, many-body degrees of freedom. These superconductors, that are described by several…
In this short note, we prove several new congruences for the overcubic partition triples function, using both elementary techniques and the theory of modular forms. These extend the recent list of such congruences given by Nayaka,…
A new mechanism for the parity doublers in hadrons is suggested.
We present an information theoretic proof of the nonsignalling multiprover parallel repetition theorem, a recent extension of its two-prover variant that underlies many hardness of approximation results. The original proofs used de Finetti…
A general approach for constructing multidimensional quasi-exactly solvable (QES) potentials with explicitly known eigenfunctions for two energy levels is proposed. Examples of new QES potentials are presented.
We give an account of the arguments that lead from the assumption of the existence of exceptional characters to the asymptotics in related ranges for the counting function of twin primes.
New, approximate, two-electron wavefunctions are introduced for the two-electron atoms (cations), which account remarkably well for the ground-state energies and the lowest-excxited states (where available). A new scheme of electronic…
To this day, the two-slit electron interference pattern remains shrouded in an inordinate mystery. It continues to defy a logical and rational explanation. This paper will postulate a new "characteristic" pertaining to the electron. If this…
Using Singular Rescaling We Prove Some Bifurcation Results. This note Presents short proofs for some Bifurcation results which had been appeared with other authors.
In this paper, a monotonicity property for the quotient of two Jacobi's theta functions with respect to the modulus $k$ is proved.
We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized eigenvalue problems of the same size as the matrices of the initial two-parameter…
We introduce a theory of multigraded Cayley-Chow forms associated to subvarieties of products of projective spaces. Two new phenomena arise: first, the construction turns out to require certain inequalities on the dimensions of projections;…
In this letter, we prove an inequality involving alternating binomial logarithmic sums by exploiting the variance of the logarithm of the maximum of independent and identically distributed exponential random variables. This inequality was…
We prove that combinatorial demand functions are characterized by two properties: continuity and the law of demand.
We introduce a new type of partitions that consists of partitions whose different parts alternate in parity (e.g., $3+2+2+1+1$). Various properties of this partition function are studied. In particular, we obtain its asymptotic behavior by…
We determine the proof-theoretic strength of the principle of countable saturation in the context of the systems for nonstandard arithmetic introduced in our earlier work.
Bi-capacities arise as a natural generalization of capacities (or fuzzy measures) in a context of decision making where underlying scales are bipolar. They are able to capture a wide variety of decision behaviours, encompassing models such…
A new characterization of conformal transformations is given. By use of this, the general form of conformal transformation on two-dimensional Minkowski space is given and its conformal structure is analyzed.