In the problem of the month 1999 : 106], one was to prove that p a + b ; c + p b + c ; a + p c + a ; b p a + p b + p c , where a, b, c are sides of a triangle. It is to be noted that this inequality will follow immediately from the Majorization Inequality 1]. Here, if A and B are vectors (a 1 a 2 : : : a n), we say that A majorizes B and write it as A B. Then, if F is a convex function, If F is...

We introduce the normalized Jensen-Mercer functional Mn( f ,x, p) = f (a)+ f (b)− n ∑ i=1 pi f (xi)− f ( a+b− n ∑ i=1 pixi ) and establish the inequalities of type MMn( f ,x,q) Mn( f ,x, p) mMn( f ,x,q) , where f is a convex function, x = (x1, . . . ,xn) and m and M are real numbers satisfying certain conditions. We prove them for the case when p and q are nonnegative n -tuples and when p and q...

T h e o r g a n i z a t i o n o f a p r o g r a m f o r l i n g u i s t i c a n a l y s i s o f g e o m e t r i c a l p a t t e r n s i s d e s c r i b e d . T h e p r o g r a m b e l o n g s t o t h e s y s t e m o f p a t t e r n r e c o g n i t i o n f o r i n d u s t r i a l d r a w i n g s a n d o b j e c t s [ 1 , 2 , 7 ] W e s t a r t e d f r o m t h e f o r m a l i s m s u g g e s t e d...

T h e o b jec t o f th is p ap e r is to p resen t ongo ing w o rk o n th e co n stru c tio n o f a m o rp hosyn tac tica lly tag g ed D an ish co rpus, w h ich is an in tegral s tep in th e m ak in g o f a C o n stra in t G ram m ar (C G ) p a rse r fo r D an ish an d a lso co n stitu te s a p a rt o f th e D an ish co n trib u tio n to th e E u ro p ean P A R O L E pro ject. T h is p ap er d ...

‎Let $R$ be a noncommutative prime ring of‎ ‎characteristic different from $2$‎, ‎$U$ the Utumi quotient ring of $R$‎, ‎$C$ $(=Z(U))$ the extended centroid‎ ‎of $R$‎. ‎Let $0neq ain R$ and $f(x_1,ldots,x_n)$ a multilinear‎ ‎polynomial over $C$ which is noncentral valued on $R$‎. ‎Suppose‎ ‎that $G$ and $H$ are two nonzero generalized derivations of $R$‎ ‎such that $a(H(f(x))f(x)-f(x)G(f(x)))in ...

The p r o b l e m s t u d i e d i s t h a t o f l e a r n i n g p r o b l e m s o l v i n g h e u r i s t i c s b y d o i n g . The pu rpose i s t o e x p l o r e t h e l e a r n i n g b e h a v i o r o f a h i g h l y c o n s t r a i n e d mechan ism. The c o n s t r a i n t s a r e choosen o n t h e b a s i s o f D s y c h o l o g i c a l c o n s i d e r a t i o n s . Computer r u n s show t ...

Suppose f(x, y) is a positive homogeneous function defined on U(j R+ × R+), call Hf (a, b; p, q) = [ f(a,b) f(aq,bq) ] 1 p−q homogeneous function with two parameters. If f(x, y) is 2nd differentiable, then the monotonicity in parameters p and q of Hf (a, b; p, q) depend on the signs of I1 = (ln f)xy , for variable a and b depend on the sign of I2a = [(ln f)x ln(y/x)]y and I2b = [(ln f)y ln(x/y)...