1,777 research outputs found
A Study on Some Fundamental Properties of Continuity and Differentiability of Functions of Soft Real Numbers
We introduce a new type of functions from a soft set to a soft set and study their properties under soft real number setting. Firstly, we investigate some properties of soft real sets. Considering the partial order relation of soft real numbers, we introduce concept of soft intervals. Boundedness of soft real sets is defined, and the celebrated theorems like nested intervals theorem and Bolzano-Weierstrass theorem are extended in this setting. Next, we introduce the concepts of limit, continuity, and differentiability of functions of soft sets. It has been possible for us to study some fundamental results of continuity of functions of soft sets such as Bolzano’s theorem, intermediate value property, and fixed point theorem. Because the soft real numbers are not linearly ordered, several twists in the arguments are required for proving those results. In the context of differentiability of functions, some basic theorems like Rolle’s theorem and Lagrange’s mean value theorem are also extended in soft setting
Particle Weights and their Disintegration I
The notion of Wigner particles is attached to irreducible unitary
representations of the Poincare group, characterized by parameters m and s of
mass and spin, respectively. However, the Lorentz symmetry is broken in
theories with long-range interactions, rendering this approach inapplicable
(infraparticle problem). A unified treatment of both particles and
infraparticles via the concept of particle weights can be given within the
framework of Local Quantum Physics. They arise as temporal limits of physical
states in the vacuum sector and describe the asymptotic particle content. In
this paper their definition and characteristic properties are worked out in
detail. The existence of the temporal limits is established by use of suitably
defined seminorms which are also essential in proving the characteristic
features of particle weights.Comment: 33 pages, amslatex, mathptm, minor corrections including numbering
schem
Measuring Multijet Structure of Hadronic Energy Flow Or What IS A Jet?
Ambiguities of jet algorithms are reinterpreted as instability wrt small
variations of input. Optimal stability occurs for observables possessing
property of calorimetric continuity (C-continuity) predetermined by kinematical
structure of calorimetric detectors. The so-called C-correlators form a basic
class of such observables and fit naturally into QFT framework, allowing
systematic theoretical studies. A few rules generate other C-continuous
observables. The resulting C-algebra correctly quantifies any feature of
multijet structure such as the "number of jets" and mass spectra of "multijet
substates". The new observables are physically equivalent to traditional ones
but can be computed from final states bypassing jet algorithms which reemerge
as a tool of approximate computation of C-observables from data with all
ambiguities under analytical control and an optimal recombination criterion
minimizing approximation errors.Comment: PostScript, 94 pp (US Letter), 18 PS files, [email protected]
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