# Objective Probabilities in Number Theoryâ€

## Related Articles

- The asymptotic distribution of a single eigenvalue gap of a Wigner matrix. Tao, Terence // Probability Theory & Related Fields;Oct2013, Vol. 157 Issue 1/2, p81
We show that the distribution of (a suitable rescaling of) a single eigenvalue gap $$\lambda _{i+1}(M_n)-\lambda _i(M_n)$$ of a random Wigner matrix ensemble in the bulk is asymptotically given by the Gaudinâ€“Mehta distribution, if the Wigner ensemble obeys a finite moment condition and...

- A new look on the truncated pentagonal number theorem. MERCA, MIRCEA // Carpathian Journal of Mathematics;2016, Vol. 32 Issue 1, p97
Two new infinite families of inequalities are given in this paper for the partition function p(n), using the truncated pentagonal number theorem.

- On the Form of the Optimal Measurement for the Probability of Detection. Wieczorek, Rafał // International Journal of Theoretical Physics;Dec2015, Vol. 54 Issue 12, p4506
We consider the problem of maximizing the probability of detection for an infinite number of mixed states. We show that for linearly independent states there exists a unique simple optimal measurement, generalizing thus a result obtained in finite dimension by Y. Eldar (Phys. Rev. A, 68,...

- A Generalization of Fortune's Conjecture. Dinculescu, A. // British Journal of Mathematics & Computer Science;2014, Vol. 4 Issue 2, p221
Fortune's Conjecture is extended from a relatively short interval after each primorial P# to an infinite numbers of similar intervals on both sides of primorials n P# , where n is a positive integer. In addition, it is shown that for every prime Py in the interval (n Pj# - Pj+1Â², nPj# +...

- On Supercyclicity of Tuples of Operators. Soltani, R.; Hedayatian, K.; Robati, B. Khani // Bulletin of the Malaysian Mathematical Sciences Society;Oct2015, Vol. 38 Issue 4, p1507
In this paper, we use a result of N. S. Feldman to show that there are no supercyclic subnormal tuples in infinite dimensions. Also, we investigate some spectral properties of hypercyclic tuples of operators. Besides, we prove that if $$T$$ is a supercyclic $$\ell $$ -tuple of commuting...

- Outage Analysis of a Multi-User Spatial Diversity System in a Shadow-Fade Propagating Channel. Emamian, Vahid // British Journal of Applied Science & Technology;2014, Vol. 4 Issue 1, p40
In a wireless network, communication between a source and a destination mobile station (DMS) fails to establish if the source or the DMS is located inside a deep shadow-fading propagating channel. In this situation, intermediate mobile stations may be used to relay the signal between the two...

- A NOTE ON KLAMKIN'S INEQUALITY. YILUN SHANG // Scientific Studies & Research. Series Mathematics & Informatics;2012, Vol. 22 Issue 2, p113
In this note, we generalize a one variable inequality of Klamkin to the case of two variables.

- Parity of the Partition Function in Arithmetic Progressions, II. Boylan, Matthew; Ono, Ken // Bulletin of the London Mathematical Society;Oct2001, Vol. 33 Issue 5, p558
Let p(n) denote the ordinary partition function. Subbarao conjectured that in every arithmetic progression r (mod t) there are infinitely many integers N = r (mod t) for which p(N) is even, and infinitely many integers M = r (mod t) for which p(M) is odd. We prove the conjecture for every...

- INFINITE LOG-MONOTONICITY OF THE CENTRAL COLUMN SEQUENCES OF COMBINATORIAL TRIANGLES. Lily Li Liu; Ya-Nan Li; Dan Ma // Journal of Combinatorics & Number Theory;2016, Vol. 8 Issue 2, p185
In this paper, we show that the infinite log-monotonicity of sequences is preserved under the componentwise product. As applications, we can obtain that the central column sequences of some classical combinatorial triangles, such as the Catalan triangles and the Narayana triangle, are infinitely...