LINEAR ISOMETRIC NON-ANTICIPATIVE TRANSFORMATIONS OF WIENER PROCESS

ThispaperisanoutcomeofnumerousdiscusionsandexchangeofideaswithlatePredragPerunicic,whosedeepandprofoundmathematicalknowledgeandhumanvaluesgaveusaninspirationandmotivationtofinalizeourjointideas.1.Wereferto[3,4]forthenotionofspectralmultiplicitytheoryintheseparableHilbertspace.LetHbeacyclicHilbertspacewiththeresolutionoftheidentity{p(t)}ofthemaximalspectraltypelIP(dt)ll'~dt-ordinaryLebesguemeasure.Anon-anticipativelineartransformationsisdefinedbyVolterrakernelg(t,u),uSt,ajsf'g(t)u)p(du),t>0…     

Tris(3,5‐di­methyl‐1H‐pyrazole‐1‐thio­carboxamidato‐κ2N2,N)­cobalt(III)

In the crystal structure of the title complex, [Co(C₆H₈N₃S)₃], the Co^III atom is octahedrally coordinated by three monodeprotonated bidentate 3,5‐di­methyl‐1H‐pyrazole‐1‐thio­carbox­amide ligands with two thio­carbox­amide N atoms in axial positions. The asymmetric unit contains two mol­ecules (A and B) and these mol­ecules are arranged in chains in an alternating fashion connected by N—H⋯S interactions.     

Whether the Support Region of Three-Bit Uniform Quantizer Has a Strong Impact on Post-Training Quantization for MNIST Dataset?

Driven by the need for the compression of weights in neural networks (NNs), which is especially beneficial for edge devices with a constrained resource, and by the need to utilize the simplest possible quantization model, in this paper, we study the performance of three-bit post-training uniform quantization. The goal is to put various choices of the key parameter of the quantizer in question (support region threshold) in one place and provide a detailed overview of this choice’s impact on the performance of post-training quantization for the MNIST dataset. Specifically, we analyze whether it is possible to preserve the accuracy of the two NN models (MLP and CNN) to a great extent with the very simple three-bit uniform quantizer, regardless of the choice of the key parameter. Moreover, our goal is to answer the question of whether it is of the utmost importance in post-training three-bit uniform quantization, as it is in quantization, to determine the optimal support region threshold value of the quantizer to achieve some predefined accuracy of the quantized neural network (QNN). The results show that the choice of the support region threshold value of the three-bit uniform quantizer does not have such a strong impact on the accuracy of the QNNs, which is not the case with two-bit uniform post-training quantization, when applied in MLP for the same classification task. Accordingly, one can anticipate that due to this special property, the post-training quantization model in question can be greatly exploited.     

Semi‐interpenetrating polymer networks composed of poly(N‐isopropyl acrylamide) and polyacrylamide hydrogels

Three series of semi‐interpenetrating polymer networks, based on crosslinked poly(N‐isopropyl acrylamide) (PNIPA) and 1 wt % nonionic or ionic (cationic and anionic) linear polyacrylamide (PAAm), were synthesized to improve the mechanical properties of PNIPA gels. The effect of the incorporation of linear polymers into responsive networks on the temperature‐induced transition, swelling behavior, and mechanical properties was studied. Polymer networks with four different crosslinking densities were prepared with various molar ratios (25:1 to 100:1) of the monomer (N‐isopropyl acrylamide) to the crosslinker (methylenebisacrylamide). The hydrogels were characterized by the determination of the equilibrium degree of swelling at 25 °C, the compression modulus, and the effective crosslinking density, as well as the ultimate hydrogel properties, such as the tensile strength and elongation at break. The introduction of cationic and anionic linear hydrophilic PAAm into PNIPA networks increased the rate of swelling, whereas the presence of nonionic PAAm diminished it. Transition temperatures were significantly affected by both the crosslinking density and the presence of linear PAAm in the hydrogel networks. Although anionic PAAm had the greatest influence on increasing the transition temperature, the presence of nonionic PAAm caused the highest dimensional change. Semi‐interpenetrating polymer networks reinforced with cationic and nonionic PAAm exhibited higher tensile strengths and elongations at break than PNIPA hydrogels, whereas the presence of anionic PAAm caused a reduction in the mechanical properties. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3987–3999, 2004     

Spatial arrangement of the structural elements ofvocal fold layers: An adjustment to the vibration process

It is well established that the multilayered structure of the vocal fold is highly adjusted to the requirements of the vibration process during phonation. There is also some partial data indicating that the spatial arrangement of each vocal fold layer corresponds to the functional requirements, and thus facilitate the phonation process. Nevertheless, all reports on the spatial arrangement of the vocal fold structures deal only with an individual element of the vocal fold histologic structure. The present study encompasses the spatial histologic analysis of all major elements of the vocal fold layers. It was demonstrated that the vocal fold epithelial cells, the connective and muscle fibers, and even the blood vessels run parallel to the vocal fold free edge, which indicates a high adjustment to the phonation requirements and the vibration process.     

A study of carrier generation in β-metal-free phthalocyanine

Photoinduced carrier generation has been studied in particle dispersions of β-metal-free phthalocyanine purified by temperature gradient sublimation. In addition to the photoconductive response measured by the delayed-collection-field technique, electric-field-induced fluorescence quenching and delayed fluorescence were also investigated. The results are consistent with the model which assumes that carrier generation proceeds through an intermediate, charge transfer (CT) state, which either dissociates into free carriers or predominantly decays to the ground state. Delayed-collection field and delayed-fluorescence experiments show that the geminate electron-hole pair is very long lived (tens of milliseconds) and has a non-exponential time decay. These results represent a new evidence for the observation of time-resolved carrier generation first reported by Mort et al. in polyvinyl carbazole. Field dependence of the geminate electron-hole pair dissociation yield is consistent with the Poole-Frenkel mechanism.     

Asymptotic aspects of Schreier graphs and Hanoi Towers groups

We present relations between growth, growth of diameters and the rate of vanishing of the spectral gap in Schreier graphs of automaton groups. In particular, we introduce a series of examples, called Hanoi Towers groups since they model the well known Hanoi Towers Problem, that illustrate some of the possible types of behavior. To cite this article: R. Grigorchuk, Z. ?unik´, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Potential Theory of Geometric Stable Processes

In this paper we study the potential theory of symmetric geometric stable processes by realizing them as subordinate Brownian motions with geometric stable subordinators. More precisely, we establish the asymptotic behaviors of the Green function and the Lévy density of symmetric geometric stable processes. The asymptotics of these functions near zero exhibit features that are very different from the ones for stable processes. The Green function behaves near zero as 1/(|x|^d log ²|x|), while the Lévy density behaves like 1/|x|^d. We also study the asymptotic behaviors of the Green function and Lévy density of subordinate Brownian motions with iterated geometric stable subordinators. As an application, we establish estimates on the capacity of small balls for these processes, as well as mean exit time estimates from small balls and a Harnack inequality for these processes. The research of this author is supported in part by MZT grant 0037118 of the Republic of Croatia and in part by a joint US-Croatia grant INT 0302167. The research of this author is supported in part by a joint US-Croatia grant INT 0302167. The research of this author is supported in part by MZT grant 0037107 of the Republic of Croatia and in part by a joint US-Croatia grant INT 0302167.