A new approach to probability theory based on quantum mechanical and Lie algebraic ideas is proposed and developed. The underlying fact is the observation that the coherent states of the Heisenberg-Weyl, su(2), su(r+1), su(1, 1) and su(r, 1) algebras in certain symmetric (bosonic) representations give the “probability amplitudes” (or the “square roots”) of the well-known Poisson, binomial, mult...

the current challenges in the management of esophageal cancer are to obtain a better understanding of underlying molecular alterations to provide new treatment options. we studied the p53 and bcl-2 protein expression in esophageal carcinomas to correlate molecular alterations with clinicopathological findings. tissue samples of 37 patients with advanced esophageal carcinoma were analyzed by imm...

darafsheh and assari in [normal edge-transitive cayley graphs onnon-abelian groups of order 4p, where p is a prime number, sci. china math. {bf 56} (1) (2013) 213$-$219.] classified the connected normal edge transitive and $frac{1}{2}-$arc-transitive cayley graph of groups of order$4p$. in this paper we continue this work by classifying theconnected cayley graph of groups of order $2pq$, $p > q...

r p c h v t … h p q p f q r t „ i b h b c q v r „ r v q p q b t c t … ‡ t w g f v c f p q b t c f ¹ p c w p c p a g f b f t … … p ˆ b a g … ¸ c h q b t c b c µ t … p f q i ˆ p q b h „ p q b v c q f † Ä c q v r c p q b t c p a Å v ¸ r t „ f g h i b p q r b h Ä c q v r ¶ b v ‚ ¹ e t a b f i ¶ v r f b t c AE † Ç † Ç † ¹ e p c b h p c w ‰ µ t r p „ i t ‡ b p à h p a v È e ‰ Ã É ¹ ´ i v Ê t w g à v ...

FcC(O)CH=C(OH)R (1, R=Me; 2, R=Fc; Fc=Fe(η5-C5H4)(η5-C5H5)) reacts with 1-H2N-4-R’-C6H4 (3 a, R‘=Me; 3 b, R‘=OMe; c, R‘=C≡N; d, R‘=F) producing β-ketoamines FcC(O)CH=C(NH(C6H4-4-R‘))R (4 a–d, 5 R=Fc). Electrochemistry shows that 4 a–d possess one a: E°′=90 mV; b: E°′=80 c: E°′=145 d: E°′=95 mV) and 5a–d two (5 E°′1,2=90, 305 E°′1,2=85, E°′1,2=155, 360 E°′1,2=105, 325 reversible redox processes....

A ring R is uniquely (nil) clean in case for any $a in R$ there exists a uniquely idempotent $ein R$ such that $a-e$ is invertible (nilpotent). Let $C =(A V W B)$ be the Morita Context ring. We determine conditions under which the rings $A,B$ are uniquely (nil) clean. Moreover we show that the center of a uniquely (nil) clean ring is uniquely (nil) clean.