On the size of the set A(A + 1)

Let F _p be the field of a prime order p. For a subset A ì F_p{A \subset F_p} we consider the product set A(A + 1). This set is an image of A ×  A under the polynomial mapping f(x, y) = xy +  x : F _p ×  F _p → F _p . In the present note we show that if |A| <  p ^1/2, then

A Remark on the Weak Topology and the Degree

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A scheme for the RCP pattern of the nano-structure

IntroductionThe balls-ffeng is a haous and dimcult problem. The meaning is the material ba1lswhich contains in it fill spare. This is an older problem. the Random-Continuous-Pile (RCP)problem. that can be trared bark to the l8th centur};'.. There are man}' unknown mysteriesin the RCP structure. With the materiaJ science de\-elopment. this old RCP problem has bee11paid attention to. Especially. in the nan(pmetre mdterial. bubble fluids. amorphous solid5.tlle RCP problem shows its titali…     

A Necessary Condition of the Cardinal

In this paper the auther begins with some known results about η_λ(=the least cardinal K such that K→(λ)~<∞), proving this theorem: If λ is not Ramsey cardinal and η_λ exists, then for every a<η_λ there is a weakly compact cardinal γ, such that λ<γ_α<η_λandγ_α<γ_βwhenever a<β<η_λ, therefore η_λ is the limit of the sequence(γ_α:a<η_λ), i.e. η_λ=limγ_α. The theorem is mainly based on the theory of models with indiscernibles.     

A Correction on the Paper of ＜A Extension of the Mitrinovit－Djokovie Inequality＞

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Some remarks concerning matrices of the form A–A′, A−1A′

Matrices and operators of the formA ^–1 A ^* have received a certain amount of attention in recent years. Here some of the literature is surveyed and the caseA ^–1 A is studied for complex matrices withA denoting the transpose ofA. A generalization ofA ^–1 A is introduced.

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Zusammenfassung Matrizen und Operatoren, die in der FormA ^–1 A ^* ausgedrückt werden können, sind in den letzten Jahren häufig studiert worden. Hier wird ein Ueberblick über Teil der relevanten Literatur gegeben und auch der FallA ^–1 A für komplexe Matrizen studiert, wobeiA die Transponierte vonA ist. Es wird auch eine Verallgemeinerung vonA ^–1 A eingeführt.

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Dedicated to Eduard Stiefel by a long time admirer     

A Remark on the Fixed point Theorem of the Expansion Mappings

Let X be a Complete metric space with distance function d, anp T a mapping from X into X. T is said to be a first type of the expansion mapping, if it satisfies the following condition