Fock spaces corresponding to positive definite linear transformations

Suppose $A$ is a positive real linear transformation on a finite dimensional complex inner product space $V$. The reproducing kernel for the Fock space of square integrable holomorphic functions on $V$ relative to the Gaussian measure $d\mu_A(z)=\frac {\sqrt {\det A}} {\pi^n}e^{-{\rm Re}} dz$ is described in terms of the holomorphic--antiholomorphic decomposition of the linear operator $A$. Moreover, if $A$ commutes with a conjugation on $V$, then a restriction mapping to the real vectors in $V$ is polarized to obtain a Segal--Bargmann transform, which we also study in the Gaussian-measure setting

Kopa nad Kompoljami pri Lukovici: gradišče in grobišče iz starejše železne dobe

A small fortified settlement or hillfort is located on Reber, a ridge rising above the village of Kompolje east of Lukovica pri Domžalah, which the excavations in 1879 showed to date to the Early Iron Age. In 2019, artefacts from the Early Iron Age also came to light on the cartway leading along the southern slopes of Kopa and Reber, the former being the peak terminating the Reber ridge in the east. The ensuing archaeological investigations by the Centre for Preventive Archaeology (2019) and the National Museum of Slovenia (2021) revealed that the finds originated from one or more inhumations. The burials were destroyed, with the exception of a part of a grave containing a ceramic jar and an iron knife, and goods scattered across the cartway deposits. Similarly scattered were human bones that belonged to at least two individuals. The grave or graves appear to have been damaged during the construction of the cartway, possibly already in 1819, when a bronze Negova helmet was also most likely found here.Na grebenasti vzpetini Reber nad vasjo Kompolje, vzhodno od Lukovice pri Domžalah, ležijo ostaline manjšega utrjenega naselja oz. gradišča. Odkritja s sondiranja leta 1879 datirajo gradišče v starejšo železno dobo. Greben Reber se na vzhodu konča z nekoliko višjo vzpetino, imenovano Kopa. Leta 2019 so na kolovozu, ki vodi po južnem pobočju Kope in Rebri, našli predmete iz starejše železne dobe. Na območju odkritja najdb so sledile arheološke raziskave Centra za preventivno arheologijo (2019) in Narodnega muzeja Slovenije (2021). Ugotovili smo, da najdbe izvirajo iz enega ali več skeletnih grobov. Razen dela zasutja grobne jame s keramičnim loncem in železnim nožem so bili pokopi uničeni, najdbe razmetane po nasutjih kolovoza, prav tako človeške kosti, ki so pripadale najmanj dvema osebama. Vse kaže, da so grob ali grobove razkopali ob gradnji kolovoza, morda že leta 1819, ko so najverjetneje prav tukaj našli bronasto negovsko čelado

Evacetrapib and Cardiovascular Outcomes in High-Risk Vascular Disease

BACKGROUND: The cholesteryl ester transfer protein inhibitor evacetrapib substantially raises the high-density lipoprotein (HDL) cholesterol level, reduces the low-density lipoprotein (LDL) cholesterol level, and enhances cellular cholesterol efflux capacity. We sought to determine the effect of evacetrapib on major adverse cardiovascular outcomes in patients with high-risk vascular disease. METHODS: In a multicenter, randomized, double-blind, placebo-controlled phase 3 trial, we enrolled 12,092 patients who had at least one of the following conditions: an acute coronary syndrome within the previous 30 to 365 days, cerebrovascular atherosclerotic disease, peripheral vascular arterial disease, or diabetes mellitus with coronary artery disease. Patients were randomly assigned to receive either evacetrapib at a dose of 130 mg or matching placebo, administered daily, in addition to standard medical therapy. The primary efficacy end point was the first occurrence of any component of the composite of death from cardiovascular causes, myocardial infarction, stroke, coronary revascularization, or hospitalization for unstable angina. RESULTS: At 3 months, a 31.1% decrease in the mean LDL cholesterol level was observed with evacetrapib versus a 6.0% increase with placebo, and a 133.2% increase in the mean HDL cholesterol level was seen with evacetrapib versus a 1.6% increase with placebo. After 1363 of the planned 1670 primary end-point events had occurred, the data and safety monitoring board recommended that the trial be terminated early because of a lack of efficacy. After a median of 26 months of evacetrapib or placebo, a primary end-point event occurred in 12.9% of the patients in the evacetrapib group and in 12.8% of those in the placebo group (hazard ratio, 1.01; 95% confidence interval, 0.91 to 1.11; P=0.91). CONCLUSIONS: Although the cholesteryl ester transfer protein inhibitor evacetrapib had favorable effects on established lipid biomarkers, treatment with evacetrapib did not result in a lower rate of cardiovascular events than placebo among patients with high-risk vascular disease. (Funded by Eli Lilly; ACCELERATE ClinicalTrials.gov number, NCT01687998 .)

Distributions on Groups of Type H

AbstractA "Fourier" transform for tempered distributions on groups of Heisenberg type is introduced. It is defined on test functions based on an automorphism group which acts transitively on the nonidentity elements of the center of the group. The transforms of homogeneous and invariant distributions are then described along with explicit results for those groups of Heisenberg type occuring for rank one simple groups

Induced group actions, representations and fibered skew product extensions

Let G G be a locally compact group acting ergodically on Y Y . We introduce the notion of an action of this group action and study the notions of induced group actions, ergodicity, and fibered product extensions in this context. We also characterize fibered skew product actions built over a cocycle.</p

Neolitizacija Krasa

The&nbsp; author&nbsp; presents&nbsp; his&nbsp; view&nbsp; of&nbsp; the&nbsp; question&nbsp; of&nbsp; theneolithisation of the Karst. It derives from analysis of the socio-historical contexts in which explanations of the neolithisationof&nbsp; the&nbsp; region&nbsp; were&nbsp; created,&nbsp; and&nbsp; through&nbsp; critical&nbsp; analysis &nbsp;ofpublished&nbsp; data&nbsp; and&nbsp; use&nbsp; of&nbsp; the&nbsp; concept&nbsp; of&nbsp; “stratigraphiccontextuality” he tries to extract a new database, on the basisof which he also provides a new picture of the process of transitionof the early Holocene hunter-gatherer communities which weredependent&nbsp; on&nbsp; biologically&nbsp; domesticated&nbsp; sources.&nbsp;Avtor predstavlja svoj pogled na vprašanje neolitizacije Krasa.Izhaja iz analize družbenozgodovinskih kontekstov, v katerihso se razlage neolitizacije regije oblikovale, ter preko kritičneanalize objavljenih podatkov in uporabe koncepta “stratigrafskekontekstualnosti”&nbsp; poskuša&nbsp; izločiti&nbsp; novo&nbsp; podatkovno&nbsp; bazo,&nbsp; napodlagi&nbsp; katere&nbsp; ponudi&nbsp; novo&nbsp; sliko&nbsp; procesa&nbsp; prehoda&nbsp; zgodnje-holocenskih lovsko-nabiralniških skupnosti v skupnosti, ki sobile&nbsp; odvisne&nbsp; od&nbsp; biološko&nbsp; udomačenih&nbsp; virov

Cocycles, extensions of group actions, and bundle representations

AbstractLet Y be an ergodic Borel G space. Conditions are determined in order for an extension X of Y to be a skew product extension of Y. These conditions depend on the behavior of the unitary bundle representation of the G space Y induced by the extension and on the existence of extensions of the G space X with certain appropriate properties

Multipliers Between Sobolev Spaces

AbstractA sufficient condition for the boundedness of a multiplier from a Sobolev space of index t &gt; 1 / 4 to one of opposite index — t is obtained. The condition relates the indices of the Sobolev spaces to which the multiplier belongs to the pairs of Sobolev spaces between which the multiplier is bounded. The result is applied to homogeneous multipliers and a description of these multipliers in this setting is presesented. Extensions to higher dimensions are indicated.</jats:p