scholarly journals A Short Note on Minimal Length

2019 ◽  
Vol 11 (2) ◽  
pp. 151-155
Author(s):  
M. Moniruzzaman ◽  
S. B. Faruque
Keyword(s):  
Hydrogen Atom ◽  
Upper Bound ◽  
Short Note ◽  
Interaction Strength ◽  
Minimal Length ◽  
Fundamental Interaction ◽  
Compton Wavelength ◽  
Nuclear Systems

After revival of the concept of minimal length, many investigations have been devoted, in literature, to estimate upper bound on minimal length for systems like hydrogen atom, deuteron etc. We report here a possible origin of minimal length for atomic and nuclear systems which is connected with the fundamental interaction strength and the Compton wavelength. The formula we appear at is numerically close to the upperbounds found in literature.

On the length of uncompletable words in unambiguous automata

2019 ◽  
Vol 53 (3-4) ◽  
pp. 115-123
Author(s):  
Antonio Boccuto ◽  
Arturo Carpi
Keyword(s):  
Upper Bound ◽  
Minimal Length ◽  
Deterministic Automaton ◽  
Transformation Monoid

This paper deals with uncomplete unambiguous automata. In this setting, we investigate the minimal length of uncompletable words. This problem is connected with a well-known conjecture formulated by A. Restivo. We introduce the notion of relatively maximal row for a suitable monoid of matrices. We show that, if M is a monoid of {0, 1}-matrices of dimension n generated by a set S, then there is a matrix of M containing a relatively maximal row which can be expressed as a product of O(n3) matrices of S. As an application, we derive some upper bound to the minimal length of an uncompletable word of an uncomplete unambiguous automaton, in the case that its transformation monoid contains a relatively maximal row which is not maximal. Finally we introduce the maximal row automaton associated with an unambiguous automaton A. It is a deterministic automaton, which is complete if and only if A is. We prove that the minimal length of the uncompletable words of A is polynomially bounded by the number of states of A and the minimal length of the uncompletable words of the associated maximal row automaton.

scholarly journals Subnomality in soluble minimax groups

1974 ◽  
Vol 17 (1) ◽  
pp. 113-128 ◽  
Author(s):  
D. J. McCaughan
Keyword(s):  
Large Class ◽  
Upper Bound ◽  
Nilpotent Groups ◽  
Subnormal Subgroup ◽  
Wreath Products ◽  
Minimal Length ◽  
Intersection Property ◽  
Finite Chain ◽  
Subnormal Subgroups

A subgroup H of a group G is said to be subnormal in G if there is a finite chain of subgroups, each normal in its successor, connecting H to G. If such chains exist there is one of minimal length; the number of strict inclusions in this chain is called the subnormal index, or defect, of H in G. The rather large class of groups which have an upper bound for the subnormal indices of their subnormal subgroups has been inverstigated to same extent, mainly with a restriction to solublegroups — for instance, in [10] McDougall considered soluble p-groups in this class. Robinson, in [14], restricted his attention to wreath products of nilpotent groups but extended his investigations to the strictly larger class of groups in which the intersection of any family of subnormal subgroups is a subnormal subgroup. These groups are said to have the subnormal intersection property.

scholarly journals Hydrogen-atom spectrum under a minimal-length hypothesis

2005 ◽  
Vol 72 (1) ◽  
Author(s):  
Sándor Benczik ◽  
Lay Nam Chang ◽  
Djordje Minic ◽  
Tatsu Takeuchi
Keyword(s):  
Hydrogen Atom ◽  
Minimal Length

scholarly journals Ground state of the hydrogen atom via Dirac equation in a minimal-length scenario

2013 ◽  
Vol 73 (7) ◽  
Author(s):  
T. L. Antonacci Oakes ◽  
R. O. Francisco ◽  
J. C. Fabris ◽  
J. A. Nogueira
Keyword(s):  
Hydrogen Atom ◽  
Dirac Equation ◽  
Ground State ◽  
Minimal Length

scholarly journals An insensitivity property of Lundberg's estimate for delayed claims

2000 ◽  
Vol 37 (03) ◽  
pp. 914-917 ◽  
Author(s):  
Pierre Brémaud
Keyword(s):  
Shot Noise ◽  
Life Insurance ◽  
Upper Bound ◽  
Short Note ◽  
Compound Poisson ◽  
Cramér’S Condition ◽  
Total Claim ◽  
Poisson Shot Noise ◽  
Ruin Problem

This short note shows that the Lundberg exponential upper bound in the ruin problem of non-life insurance with compound Poisson claims is also valid for the Poisson shot noise delayed-claims model, and that the optimal exponent depends only on the distribution of the total claim per accident, not on the time it takes to honour the claim. This result holds under Cramer's condition.

scholarly journals A Note on Odd Cycle-Complete Graph Ramsey Numbers

10.37236/1662 ◽  
2001 ◽  
Vol 9 (1) ◽  
Author(s):  
Benny Sudakov
Keyword(s):  
Positive Integer ◽  
Complete Graph ◽  
Upper Bound ◽  
Short Note ◽  
Ramsey Number ◽  
Ramsey Numbers ◽  
Odd Cycle

The Ramsey number $r(C_l, K_n)$ is the smallest positive integer $m$ such that every graph of order $m$ contains either cycle of length $l$ or a set of $n$ independent vertices. In this short note we slightly improve the best known upper bound on $r(C_l, K_n)$ for odd $l$.

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