Renormalization of potentials and generalized centers

We generalize the Riesz potential of a compact domain in $\mathbb{R}^{m}$ by introducing a renormalization of the $r^{\alpha-m}$-potential for $\alpha\le0$. This can be considered as generalization of the dual mixed volumes of convex bodies as introduced by Lutwak. We then study the points where the extreme values of the (renormalized) potentials are attained. These points can be considered as a generalization of the center of mass. We also show that only balls give extreme values among bodied with the same volume.Comment: Adv. Appl. Math. 48 (2012), 365--392 Figure 11 has been corrected after publication. Theorem 3.12 and the exposition of Lemma 2.15 are modified in version

Non-compact QED(3) coupled to a four-fermi interaction

We present preliminary numerical results for the three dimensional non-compact QED with a weak four-fermion term in the lattice action. Approaches based on Schwinger-Dyson studies, arguments based on thermodynamic inequalities and numerical simulations lead to estimates of the critical number of fermion flavors (below which chiral symmetry is broken) ranging from $N_{fc}=1$ to $N_{fc}=4$. The weak four-fermion coupling provides the framework for an improved algorithm, which allows us to simulate the chiral limit of massless fermions and expose delicate effects.Comment: 3 pages, Contribution to Lattice2004(chiral), Fermilab, June 21-26, 200

Statuta Regni Poloniae in Ordinem alphabeti digesta

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Aqueous extracts from some muscles inhibit hemoglobin-mediated oxidation of cod muscle membrane lipids

It was evaluated whether trout hemoglobin (Hb)-mediated oxidation of minced washed cod muscle lipids could be prevented by an aqueous isolate from cod and some other muscle sources. Lipid hydroperoxides and painty odor developed ∼4 days faster in washed than unwashed cod mince. When adding back an aqueous fraction (press juice) isolated from unwashed mince to washed mince at 2−6-fold dilutions, development of hydroperoxides and painty odor was either delayed or completely prevented. The inhibitory substances were heat stable, and their effect was slightly reduced at reduced pH. Th

On Point Sets fixing a Convex Body from within

: We study the concept of a set fixing a convex body from within that was recently proposed by V. Soltan. We prove his conjecture that a finite set which fixes a d-dimensional convex body from within contains a subset of at most 2d points with the same property. 1. Introduction The classical definition [2],[4] of a set S fixing a convex body K ae R d is that S ae K and for each translation by a vector t 2 R d , t 6= 0 there is a point s 2 S and an " ? 0 such that s = 2 interior K but s 2 interior(K + "t). This models a solid object K which is held in its place (against translations) by some points S outside K which would have to move inside K if one tried to force a movement. At the 1995 Intuitive Geometry Conference, V. Soltan defined a new concept of a fixing set. He calls a set S fixing the convex body K ae R d from within if S ae K and for each translation t 6= 0 there is an s 2 S such that s = 2 K + t. This models a rigid surface @K held in its place by some points S insi..

Chronica Sive Historiae Polonicae Compendiosa, Ac Per Certa Librorum Capita ad facilem memoriam recens facta descriptio

CHRONICA SIVE HISTORIAE POLONICAE COMPENDIOSA, AC PER CERTA LIBRORUM CAPITA AD FACILEM MEMORIAM RECENS FACTA DESCRIPTIO Chronica Sive Historiae Polonicae Compendiosa, Ac Per Certa Librorum Capita ad facilem memoriam recens facta descriptio ( - ) Einband ( - ) Titelseite ([1]) Epistola Dedicatoria ([2]) Liber I (1) Liber II (22) Liber III (38) Liber IV (59) Liber V (95) Liber VI (126) Liber VII (147) Liber VIII (177) Liber IX (189) Liber X (214) Liber XI (235) Liber XII (248) Liber XIII (269) Liber XIV (296) Liber XV (333) Liber XVI (365) Liber XVII (407) Liber XVIII (440) Liber XIX (453) Liber XX (467) Index ([1]