On Bounded Strictly Positive Operators of Closed Range and Some Applications to Asymptotic Hyperstability of Dynamic Systems

The problem discussed is the stability of two input-output feedforward and feedback relations, under an integral-type constraint defining an admissible class of feedback controllers. Sufficiency-type conditions are given for the positive, bounded and of closed range feed-forward operator to be strictly positive and then boundedly invertible, with its existing inverse being also a strictly positive operator. The general formalism is first established and the linked to properties of some typical contractive and pseudocontractive mappings while some real-world applications and links of the above formalism to asymptotic hyperstability of dynamic systems are discussed later on.

On a Class of Self-Adjoint Compact Operators in Hilbert Spaces and Their Relations with Their Finite-Range Truncations

This paper investigates a class of self-adjoint compact operators in Hilbert spaces related to their truncated versions with finite-dimensional ranges. The comparisons are established in terms of worst-case norm errors of the composite operators generated from iterated computations. Some boundedness properties of the worst-case norms of the errors in their respective fixed points in which they exist are also given. The iterated sequences are expanded in separable Hilbert spaces through the use of numerable orthonormal bases.

The Voltage-Gated Sodium Channel Na(v)1.8 Is Expressed in Human Sperm

The role of Na+ fluxes through voltage-gated sodium channels in the regulation of sperm cell function remains poorly understood. Previously, we reported that several genes encoding voltage-gated Na+ channels were expressed in human testis and mature spermatozoa. In this study, we analyzed the presence and function of the TTX-resistant VGSC a subunit Na(v)1.8 in human capacitated sperm cells. Using an RT-PCR assay, we found that the mRNA of the gene SCN10A, that encode Na-v1.8, was abundantly and specifically expressed in human testis and ejaculated spermatozoa. The Na-v1.8 protein was detected in capacitated sperm cells using three different specific antibodies against this channel. Positive immunoreactivity was mainly located in the neck and the principal piece of the flagellum. The presence of Na-v1.8 in sperm cells was confirmed by Western blot. Functional studies demonstrated that the increases in progressive motility produced by veratridine, a voltage-gated sodium channel activator, were reduced in sperm cells preincubated with TTX (10 mu M), the Na-v1.8 antagonist A-803467, or a specific Na-v1.8 antibody. Veratridine elicited similar percentage increases in progressive motility in sperm cells maintained in Ca2+-containing or Ca2+-free solution and did not induce hyperactivation or the acrosome reaction. Veratridine caused a rise in sperm intracellular Na+, [Na+](i), and the sustained phase of the response was inhibited in the presence of A-803467. These results verify that the Na+ channel Na-v1.8 is present in human sperm cells and demonstrate that this channel participates in the regulation of sperm function.

Results on proximal and generalized weak proximal contractions including the case of iteration-dependent range sets

This paper presents some further results on proximal and asymptotic proximal contractions and on a class of generalized weak proximal contractions in metric spaces. The generalizations are stated for non-self-mappings of the forms for and , or , subject to and , such that converges uniformly to T, and the distances are iteration-dependent, where , , and are non-empty subsets of X, for , where is a metric space, provided that the set-theoretic limit of the sequences of closed sets and exist as and that the countable infinite unions of the closed sets are closed. The convergence of the sequences in the domain and the image sets of the non-self-mapping, as well as the existence and uniqueness of the best proximity points, are also investigated if the metric space is complete. Two application examples are also given, being concerned, respectively, with the solutions through pseudo-inverses of both compatible and incompatible linear algebraic systems and with the parametrical

The Carpathian range represents a weak genetic barrier in South-East Europe

Background: In the present study we have assessed whether the Carpathian Mountains represent a genetic barrier in East Europe. Therefore, we have analyzed the mtDNA of 128 native individuals of Romania: 62 of them from the North of Romania, and 66 from South Romania. Results: We have analyzed their mtDNA variability in the context of other European and Near Eastern populations through multivariate analyses. The results show that regarding the mtDNA haplogroup and haplotype distributions the Romanian groups living outside the Carpathian range (South Romania) displayed some degree of genetic differentiation compared to those living within the Carpahian range (North Romania). Conclusion: The main differentiation between the mtDNA variability of the groups from North and South Romania can be attributed to the demographic movements from East to West (prehistoric or historic) that differently affected in these regions, suggesting that the Carpathian mountain range represents a weak genetic barrier in South-East Europe.

CGP37157, an inhibitor of the mitochondrial Na+/Ca2+ exchanger, protects neurons from excitotoxicity by blocking voltage-gated Ca2+ channels

Inhibition of the mitochondrial Na+/Ca2+ exchanger (NCLX) by CGP37157 is protective in models of neuronal injury that involve disruption of intracellular Ca2+ homeostasis. However, the Ca2+ signaling pathways and stores underlying neuroprotection by that inhibitor are not well defined. In the present study, we analyzed how intracellular Ca2+ levels are modulated by CGP37157 (10 mu M) during NMDA insults in primary cultures of rat cortical neurons. We initially assessed the presence of NCLX in mitochondria of cultured neurons by immunolabeling, and subsequently, we analyzed the effects of CGP37157 on neuronal Ca2+ homeostasis using cameleon-based mitochondrial Ca2+ and cytosolic Ca2+ ([Ca2+](i)) live imaging. We observed that NCLX-driven mitochondrial Ca2+ exchange occurs in cortical neurons under basal conditions as CGP37157 induced a decrease in [Ca-2](i) concomitant with a Ca2+ accumulation inside the mitochondria. In turn, CGP37157 also inhibited mitochondrial Ca2+ efflux after the stimulation of acetylcholine receptors. In contrast, CGP37157 strongly prevented depolarization-induced [Ca2+](i) increase by blocking voltage-gated Ca2+ channels (VGCCs), whereas it did not induce depletion of ER Ca2+ stores. Moreover, mitochondrial Ca2+ overload was reduced as a consequence of diminished Ca2+ entry through VGCCs. The decrease in cytosolic and mitochondrial Ca2+ overload by CGP37157 resulted in a reduction of excitotoxic mitochondrial damage, characterized here by a reduction in mitochondrial membrane depolarization, oxidative stress and calpain activation. In summary, our results provide evidence that during excitotoxicity CGP37157 modulates cytosolic and mitochondrial Ca2+ dynamics that leads to attenuation of NMDA-induced mitochondrial dysfunction and neuronal cell death by blocking VGCCs.