We asymptotically determine the size of the largest family F of subsets of {1, . . . , n} not containing a given poset P if the Hasse diagram of P is a tree. This is a qualitative generalization of several known results including Sperner’s theorem. Introduction We say that a poset P is a subposet of a poset P ′ if there is an injective map f : P → P ′ such that a 6P b implies f(a) 6P ′ f(b). A ...

J. Pereira∗a,b, A. Aprahamianc,d, O. Arndte, f , A. Becerrila,b, T. Elliota,b, A. Estradea,b,g, D. Galaviza,b, S. Hennriche, f ,a, R. Kesslere, f ,a, K.-L. Kratz f ,h, G. Lorussoa,b,g, P.F. Manticaa,i, M. Matosa,b, F. Montesa,b,g, P. Santia,b, B. Pfeiffer f ,h, M. Quinnc,d, H. Schatza,b,g, F. Schertze, f ,a, L. Schnorrenbergera,b, j, E. Smithb,k, B.E. Tomlina,i, W. Waltersl, A. Wöhrc,d aNationa...

The scheme ChoiceD concerns a non-empty set A, a non-empty set B, and a binary predicate P, and states that: there exists a function h from A into B such that for every element a of A holds P[a, h(a)] provided the parameters meet the following requirement: • for every element a of A there exists an element b of B such that P[a, b]. Let A, B, C be non-empty sets, and let f be a function from A i...

This note presents a method to study center families of periodic orbits of complex holomorphic differential equations near singularities, based on some iteration properties of fixed point indices. As an application of this method, we will prove Needham’s theorem in a more general version. 1. Fixed point indices of holomorphic mappings Let C be the complex vector space of dimension n, let U be a...

Let P : F × F → F be a polynomial of bounded degree over a finite field F of large characteristic. In this paper we establish the following dichotomy: either P is a moderate asymmetric expander in the sense that |P (A,B)| |F| whenever A,B ⊂ F are such that |A||B| ≥ C|F|2−1/8 for a sufficiently large C, or else P takes the form P (x, y) = Q(F (x) + G(y)) or P (x, y) = Q(F (x)G(y)) for some polyn...

A b s t r a c t T h e p a p e r i s a i m e d a t e x a m i n i n g t h e r e l a t i o n s h i p b e t w e e n t h e t h r e e t o p i c s o f t h e w o r k s h o p s t h a t g a v e r i s e t o t h i s b o o k : s e c u r i t y , f a u l t t o l e r a n c e , a n d s o f t w a r e a s s u r a n c e. T h o s e t h r e e t o p i c s c a n b e v i e w e d a s d i f f e r e n t f a c e t s o f d ...

In the present paper we prove the Chebyshev inequality involving two isotonic linear functionals. Namely, if A and B are isotonic linear functionals, then A(p f g)B(q)+A(p)B(q f g) A(p f )B(qg) + A(pg)B(q f ) , where p,q are non-negative weights and f ,g are similarly ordered functions such that the above-mentioned terms are well-defined. If functionals are equal, i.e. A = B and if p = q , then...

Humans can r e c o v e r t h e shape o f a s u r f a c e f r o m i t s image b o u n d a r y . The a u t h o r s have p r e s e n t e d a new a p p r o a c h t o shape f r o m b o u n d a r y [ 4 ] . I t i n c l u d e s t h r e e p o i n t s : t h e l i n e o f c u r v a t u r e (LOC) r e g u l a r i t y , a n a l g o r i t h m f o r c o n s t r u c t i n g LOC net f r o m b o u n d a r y , and...