Search results for "7a"
showing 10 items of 161 documents
Frame-related Sequences in Chains and Scales of Hilbert Spaces
2022
Frames for Hilbert spaces are interesting for mathematicians but also important for applications in, e.g., signal analysis and physics. In both mathematics and physics, it is natural to consider a full scale of spaces, and not only a single one. In this paper, we study how certain frame-related properties of a certain sequence in one of the spaces, such as completeness or the property of being a (semi-) frame, propagate to the other ones in a scale of Hilbert spaces. We link that to the properties of the respective frame-related operators, such as analysis or synthesis. We start with a detailed survey of the theory of Hilbert chains. Using a canonical isomorphism, the properties of frame se…
Frames and weak frames for unbounded operators
2020
In 2012 G\u{a}vru\c{t}a introduced the notions of $K$-frame and of atomic system for a linear bounded operator $K$ in a Hilbert space $\mathcal{H}$, in order to decompose its range $\mathcal{R}(K)$ with a frame-like expansion. In this article we revisit these concepts for an unbounded and densely defined operator $A:\mathcal{D}(A)\to\mathcal{H}$ in two different ways. In one case we consider a non-Bessel sequence where the coefficient sequence depends continuously on $f\in\mathcal{D}(A)$ with respect to the norm of $\mathcal{H}$. In the other case we consider a Bessel sequence and the coefficient sequence depends continuously on $f\in\mathcal{D}(A)$ with respect to the graph norm of $A$.
Hilbert space operators with two-isometric dilations
2021
A bounded linear Hilbert space operator $S$ is said to be a $2$-isometry if the operator $S$ and its adjoint $S^*$ satisfy the relation $S^{*2}S^{2} - 2 S^{*}S + I = 0$. In this paper, we study Hilbert space operators having liftings or dilations to $2$-isometries. The adjoint of an operator which admits such liftings is characterized as the restriction of a backward shift on a Hilbert space of vector-valued analytic functions. These results are applied to concave operators (i.e., operators $S$ such that $S^{*2}S^{2} - 2 S^{*}S + I \le 0$) and to operators similar to contractions or isometries. Two types of liftings to $2$-isometries, as well as the extensions induced by them, are construct…
CCDC 868802: Experimental Crystal Structure Determination
2012
Related Article: A.Cornia, F.Felluga, V.Frenna, F.Ghelfi, A.F.Parsons, M.Pattarozzi, F.Roncaglia, D.Spinelli|2012|Tetrahedron|68|5863|doi:10.1016/j.tet.2012.04.117
CCDC 262065: Experimental Crystal Structure Determination
2006
Related Article: G.Stajer, A.E.Szabo, G.Turos, P.Sohar, R.Sillanpaa|2005|Eur.J.Org.Chem.|2005|4154|doi:10.1002/ejoc.200500155
Angiopoietin-Like Protein 8 Is a Novel Vitamin D Receptor Target Gene Involved in Nonalcoholic Fatty Liver Pathogenesis
2018
Hepatic vitamin D receptor (VDR) expression is increased in patients with nonalcoholic fatty liver (NAFL) and is required for liver steatosis in an NAFL mouse model. However, how hepatocyte VDR is involved in setting up steatosis remains unclear. The authors transduced human hepatocyte-derived cells with an adenoviral vector encoding human VDR and found that angiopoietin-like protein 8 (ANGPTL8) expression was increased upon VDR activation by vitamin D or lithocholic acid. The mRNA levels of hepatic VDR- and vitamin D-related genes [cytochrome P450 (CYP) 2R1, CYP27A1, and CYP3A4] were higher in NAFL patients compared with normal liver subjects. Noteworthy, hepatic ANGPTL8 mRNA and protein l…
Specific association of IL17A genetic variants with panuveitis.
2015
Background/aims A pathogenic role of Th17 cells in uveitis has become clear in recent years. Therefore, in the present study, we aimed to evaluate the possible influence of the IL 17A locus on susceptibility to non-anterior uveitis and its main clinical subgroups. Methods Five IL17A polymorphisms (rs4711998, rs8193036, rs3819024, rs2275913 and rs7747909), selected by tagging, were genotyped using TagMan assays in 353 Spanish patients with non-anterior uveitis and 1851 ethnically matched controls. Results The case/control analysis yielded a consistent association between two of the analysed genetic variants, rs8193036 and rs2275913, and the presence of panuveitis under a dominant model (p(FD…
Analysis of serum and endometrial progesterone in determining endometrial receptivity.
2021
Abstract STUDY QUESTION Is there a relationship between serum and endometrial progesterone (P4) levels, including P4 and metabolites (oestrone, oestradiol and 17α-hydroxyprogesterone), and endometrial receptivity? SUMMARY ANSWER Serum P4 levels were not correlated with endometrial P4, nor associated with endometrial receptivity as determined by the ERA® test; however, endometrial P4 and 17α-hydroxyprogesterone levels were positively correlated and related to endometrial receptivity by ERA. WHAT IS KNOWN ALREADY Acquisition of endometrial receptivity is governed by P4, which induces secretory transformation. A close relationship between serum P4 and pregnancy outcome is reported for hormone …
Supersymmetric structures for second order differential operators
2012
Necessary and sufficient conditions are obtained for a real semiclassical partial differential operator of order two to possess a supersymmetric structure. For the operator coming from a chain of oscillators, coupled to two heat baths, we show the non-existence of a smooth supersymmetric structure, for a suitable interaction potential, provided that the temperatures of the baths are different.
PDZD7 connects the Usher protein complex to the intraflagellar transport machinery
2015
Several Usher syndrome (USH)-associated proteins are known to localize to the connecting cilium of photoreceptor cells. The unconventional myosin MYO7A (USH1B) was long accepted as the transport molecule responsible for the ciliary localization of USH proteins. However, based on the typical location of several of the USH proteins along the ciliary axoneme, the involvement of the main ciliary trafficking machinery, intraflagellar transport (IFT), seems apparent. The USH-associated scaffold protein PDZD7 is known to interact with SANS, Usherin, GPR98 and Whirlin, all of which can be found in the connecting cilium. Here, we report that PDZD7 provides the physical link of the USH-protein networ…