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Main purpose of this paper is to formulate canonical quantum continuity equations for white noise operators and to find their explicit unique solutions. By applying the continuity equations for white noise functionals and canonical topological isomorphisms between the spaces of white noise operators and the spaces of two-variable white noise functionals, we formulate canonical quantum continuity equations for white noise operators, and then we induce time dependent quantum evolution systems which are equivalent to the quantum continuity equations. Then we find explicit forms, in terms of the quantum analogues of generalized Fourier-Mehler transforms, of the unique solutions of the quantum continuity equations by solving the quantum evolution systems for white noise operators. [ABSTRACT FROM AUTHOR]

Introducing a segregated network constructed through the selective localization of small amounts of fillers can be a solution to overcome the limitations of the practical use of graphene-based conductive composites due to the high cost of fillers. In this study, polypropylene composites filled with randomly dispersed GNPs and a segregated GNP network were prepared, and their conductive properties were investigated according to the formation of the segregated structure. Due to the GNP clusters induced by the segregated structure, the electrical percolation threshold was 2.9 wt% lower than that of the composite incorporating randomly dispersed GNPs. The fully interconnected GNP cluster network inside the composite contributed to achieving the thermal conductivity of 4.05 W/m∙K at 10 wt% filler content. Therefore, the introduction of a segregated filler network was suitable to simultaneously achieve excellent electrical and thermal conductivities at a low content of GNPs.

Based on the quantum white noise theory, we formulate new types of anticipating quantum stochastic integrals by combining the Hitsuda–Skorokhod quantum stochastic integrals and the interactions between the integrands and the integrators. For our purpose, we prove various versions of analytic characterization theorems of symbols of white noise operators as more general cases. Also, several types of quantum (stochastic) gradients are formulated as continuous linear operators which are related to the quantum white noise derivatives and reflecting the interactions with the external noises. Finally, we formulate further systematical study of anticipating quantum stochastic integrals. [ABSTRACT FROM AUTHOR]

Microarray technology represents a critical new advance in molecular cytogenetics. The de-velopment of this approach has provided fundamental insights into the molecular pathogenesis in clinical cytogenetics and has provided a clue to many unidentified or unexplained diseases. The approach allows a comprehensive investigation of thousands and millions of genomic loci simultaneously and enables the efficient detection of copy number alterations. The application of this technology has shown tremendous fluidity and complexity of the human genome, and has provided accurate diagnosis and appropriate clinical management in a timely and efficient manner for identifying genomic alterations. The clinical impact of the genomic alterations identified by microarrays is evolving into a diagnostic tool to identify high-risk patients better and predict patient outcomes from their genomic profiles. The transformation of conventional cytogenetics into an automated discipline will improve diagnostic yield significantly, leading to accurate diagnosis and genetic counseling. This article reviews cytogenetic technologies used to identify human chromosome alterations and highlights the potential utility of present and future genome microarray technology in the diagnosis.

Background Recent studies have reported high rates of recurrence of shoulder instability in patients with glenoid bone defects greater than 20% after capsulolabral reconstruction. The purpose of the present study was to evaluate the failure rate of arthroscopic capsulolabral reconstruction for the treatment of anterior instability in the presence of glenoid bone deficits >20%. Methods Retrospective analyses were conducted among cases with anterior shoulder instability and glenoid bone defects of >20% that were treated by arthroscopic capsulolabral reconstruction with a minimum 2-year follow-up (30 cases). We included the following variables: age, bone defect size, instability severity index score (ISIS), on-/off-track assessment, incidence recurrent instability, and return to sports. Results The mean glenoid bone defect size was 25.8%±4.2% (range, 20.4%–37.2%), and 18 cases (60%) had defects of >25%. Bony Bankart lesions were identified in 11 cases (36.7%). Eleven cases (36.7%) had ISIS scores >6 points and 21 cases (70%) had off-track lesions. No cases of recurrent instability were identified over a mean follow-up of 39.9 months (range, 24–86 months), but a sense of subluxation was reported by three patients. Return to sports at the preinjury level was possible in 24 cases (80%), and the average satisfaction rating was 92%. Conclusions Arthroscopic soft tissue reconstruction was successful for treating anterior shoulder instability among patients with glenoid bone defects >20%, even enabling return to sports. Future studies should focus on determining the range of bone defect sizes that can be successfully managed by soft tissue repair.

Riparian vegetation plays a fundamental role in alluvial channel evolution by modifying flow and sedimentation dynamics. To elucidate the roles of sediment supply, flow‐dependent transport capacity, and morphodynamic feedbacks on the evolution of emergent vegetation patches over a single hydrograph, we conducted two experiments with different reach‐scale sediment supplies: a high‐supply experiment (HSE) and low‐supply experiment (LSE). We measured flow velocities, bedload transport, and topographic changes around a full‐scale patch of live emergent willows in an outdoor laboratory flume. Erosion occurred in the patch‐adjacent channel areas irrespective of the sediment supply, whereas deposition within the patch interior was suppressed in the LSE and enhanced in the HSE. The magnitude of patch deposition in each experiment was controlled by the local sediment supply to the patch and local sediment mobility during each discharge in the hydrograph. The local sediment supply was affected by bed morphodynamics at the patch head, which modulated the reach‐scale sediment supply by redistributing the bedload in the channel. Sediment mobility within the patch was flow‐dependent and a function of velocity and turbulent kinetic energy. For different discharges, the velocity in the patch changed proportionally with the freestream velocity; however, the turbulent kinetic energy was more sensitive, being elevated compared with the freestream during high flows and inhibited at low flows. Therefore, deposition and erosion within vegetation patches are not simply functions of the reach‐scale sediment supply or patch flow characteristics, as is often assumed, but additionally depend on the local sediment supply to the patch interior. Plain Language Summary: Riparian vegetation in rivers and deltas is considered a primary cause of sediment deposition and channel stabilization. However, in the laboratory, we identified the physical mechanisms influencing sediment deposition and erosion and their change over a natural flow regime to illustrate that the same full‐sized willow patch can either enhance or reduce sediment deposition within the patch interior relative to the same channel without vegetation. The amount of sediment deposited in the vegetation patch depended on the velocity and turbulent kinetic energy of the water, which changed as the flow decreased. Additionally, the presence of a single vegetation patch fundamentally changed the character of the channel from depositional to erosional near the patch, indicating that more erosion occurred in adjacent channels than deposition within the patch. Deposition and erosion of the bed were also influenced by the amount of sediment supplied to the channel from upstream. This reach‐scale sediment supply was modified by a sediment mound that formed at the upstream end of the patch during high sediment supply to the channel. The mound redistributed the sediment transport within the channel and vegetation patch, revealing another physical mechanism influencing the spatial and temporal variability of bedload transport in vegetated channels. Key Points: Relative to the open depositional channel located upstream, a single vegetation patch caused channel erosion that lowered the median bed elevations by up to 640%The same vegetation patch can both inhibit and enhance interior sediment deposition depending on the flow‐dependent transport capacity and local sediment supplyMorphodynamic bed changes modulated the reach‐scale sediment supply in and around the patch by spatially redistributing bedload within the channel [ABSTRACT FROM AUTHOR]

In this study, the thermal percolation behavior for the thermal conductivity of nanocomposites according to the lateral size of graphene nanoplatelets (GNPs) was studied. When the amount of GNPs reached the critical concentration, a rapid increase in thermal conductivity and thermal percolation behavior of the nanocomposites were induced by the GNP network. Interestingly, as the size of GNPs increased, higher thermal conductivity and a lower percolation threshold were observed. The in-plane thermal conductivity of the nanocomposite containing 30 wt.% M25 GNP (the largest size) was 8.094 W/m·K, and it was improved by 1518.8% compared to the polymer matrix. These experimentally obtained thermal conductivity results for below and above the critical content were theoretically explained by applying Nan’s model and the percolation model, respectively, in relation to the GNP size. The thermal percolation behavior according to the GNP size identified in this study can provide insight into the design of nanocomposite materials with excellent heat dissipation properties.

We investigate the convergence of higher order Cesàro means in Banach spaces. The main results of this paper are: (1) The proof of mean and Birkhoff-type ergodic theorems for higher order Cesàro means. (2) The existence of a one-to-one correspondence between convergent Cesàro means of different orders. (3) The proof of strong laws of large numbers for higher order sums of independent and identically distributed random elements. (4) A characterization of the ergodicity of measure preserving maps in terms of higher order mixing properties. To deal with higher order Cesàro means, one needs a notion of weighted mean more general than the one usually considered in the literature on weighted ergodic theorems. In this context, we also prove a characterization of generalized weighted means preserving Cesàro convergence. [ABSTRACT FROM AUTHOR]