相关论文: A New Theorem Relating the Tangent Secant Theorem …
The resource theory of coherence studies the operational value of superpositions in quantum technologies. A key question in this theory concerns the efficiency of manipulation and interconversion of this resource. Here we solve this…
If a one-variable function is sufficiently smooth, then the limit position of secant lines its graph is a tangent line. By analogy, one would expect that the limit position of secant planes of a two-variable smooth function is a plane…
We study the relationship between the equations defining a projective variety and properties of its secant varieties. In particular, we use information about the syzygies among the defining equations to derive smoothness and normality…
Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…
We provide self-contained proof of a theorem relating probabilistic coherence of forecasts to their non-domination by rival forecasts with respect to any proper scoring rule. The theorem appears to be new but is closely related to results…
A cornerstone of the theory of cohomology jump loci is the Tangent Cone theorem, which relates the behavior around the origin of the characteristic and resonance varieties of a space. We revisit this theorem, in both the algebraic setting…
The notion of the quantum angle is introduced. The quantum angle turns out to be a metric on the set of physical states of a quantum system. Its kinematics and dynamics is studied. The certainty principle for quantum systems is formulated…
Regardless of the gold-standard being considered as outdated, it provides valuable signs concerning the development of novel monetary standards, better adjusted to the current macroeconomic environment. By using a point of view of classical…
In this paper, we shed light on relations between three concepts studied in representations theory, algebraic geometry and quantum information theory. First - spherical actions of reductive groups on projective spaces. Second - secant…
The effects of decoherence for quantum system coupled with a bosonic field are investigated. An application of the stochastic golden rule shows that in the stochastic limit the dynamics of such a system is described by a quantum stochastic…
An unconditional inequality of the totient function is contributed to the literature. This result is associated with various problems about the distribution of prime numbers.
The theoretical foundations of the phenomenon known as super-radiance still continues to attract considerable attention. Despite many valiant attempts at pedagogically clear presentations, the effect nevertheless still continues to generate…
We establish some new theorems on pentagon and pentagram.
Simple methods permit to generalize the concepts of iteration and of recursive processes. We shall see briefly on several examples what these methods generate. In additive sequences, we shall encounter not only the golden or the silver…
The pursue of what are properties that can be identified to permit an automated reasoning program to generate and find new and interesting theorems is an interesting research goal (pun intended). The automatic discovery of new theorems is a…
Let $\alpha=(1+\sqrt 5)/2$, the golden ratio, and $\beta=-1/\alpha=(1 - \sqrt 5)/2$. Let $F_n$ and $L_n$ be the Fibonacci and Lucas numbers, defined by $F_n=(\alpha^n -\beta^n)/\sqrt 5$ and $L_n=\alpha^n + \beta^n$, for all non-negative…
A new apparent relativistic paradox is presented involving only one space-time event. This is different from earlier relativistic paradoxes involving extended bodies or events at different positions. A collision between a rod and a ring…
A quotient of a poset $P$ is a partial order obtained on the equivalence classes of an equivalence relation $\theta$ on $P$; $\theta$ is then called a congruence if it satisfies certain conditions, which vary according to different…
We formulate the Secant Conjecture, which is a generalization of the Shapiro Conjecture for Grassmannians. It asserts that an intersection of Schubert varieties in a Grassmannian is transverse with all points real, if the flags defining the…
In this work, we develop Extraction Theorems for classes of geometric objects with small extraction numbers. These classes include intervals, axis-parallel segments, axis-parallel rays, and octants. We investigate these classes of objects…