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In this paper, we study the stochastic heat equation (SHE) on $\mathbb{R}^d$ subject to a centered Gaussian noise that is white in time and colored in space. We establish the existence and uniqueness of the random field solution in the presence of locally Lipschitz drift and diffusion coefficients, which can have certain superlinear growth. This is a nontrivial extension of the recent work by Dalang, Khoshnevisan and Zhang (2019), where the one-dimensional SHE on $[0,1]$ subject to space-time white noise has been studied., Comment: 15 pages

Microbial fuel cell (MFC) is lauded for its capacity to valorize organic substrates in wastes, providing a solution to environmental pollution and energy crisis. While different types of organic substrates affect removal efficiency and current output, most MFCs are designed to only be able to utilize one type of wastewater. However, many real wastewater treatment sites generate more than one type of wastewater which hinders the installation of most MFCs. This study aimed to investigate the performance of the novel-designed multi-anode shared cathode MFC (MASC-MFC) compared with a standard single anode/cathode MFC (SAC-MFC) and the simultaneous treatment of different types of real wastewaters (sewage, slaughterhouse, and hospital) in one MFC unit. The MASC-MFC (9025 mW/m

Constructed wetland coupled microbial fuel cell (CW-MFC) systems integrate an aerobic zone and an anaerobic zone to treat wastewater and to generate bioenergy. The concept evolves based on the principles of constructed wetlands and plant MFC (one form of photosynthetic MFC) technologies, of which all contain plants. CW-MFC have been used in a wide range of application since their introduction in 2012 for wastewater treatment and electricity generation. However, there are few reports on the individual components and their performance on CW-MFC efficiency. The performance and efficiency of this technology are significantly influenced by several factors such as the organic load and sewage composition, hydraulic retention time, cathode dissolved oxygen, electrode materials and wetland plants. This paper reviews the influence of the macrophyte (wetland plants) component, substrate material, microorganisms, electrode material and hydraulic retention time (HRT) on CW-MFC performance in wastewater treatment and electricity generation. The study assesses the relationship between these parameters and discusses progress in the development of this integrated system to date.

Microbial desalination cells (MDC) syndicate the advantage of physical separation by using membranes to create conditions required for Bioelectrochemical processes for the treatment of various domestic and industrial wastewater, while simultaneously desalinating saline water and generating bioenergy. However, since the introduction of this technology, heavy metal removal has been a challenge, and membrane fouling has become a major bottleneck limiting the optimum performance and efficiency of this technology. This study incorporated the use of ZIF-8 nanocomposite membrane via phase inversion mechanism in MDC for simultaneous heavy metal removal and membrane biofouling prevention. The study was conducted in two MDC systems; MDC-Control (without the ZIF-8 nanocomposite membrane) and MDC with ZIF-8 nanocomposite membrane. The results from the experiment shown that maximum removal efficiency of 85.7%, 84.3%, 84.0%, and 90.61% was obtained for Cu

Although significant progress has been made in the self-assembly of nanostructures, present successes heavily rely on precision in building block design, composition, and pair interactions. These requirements fundamentally limit our ability to synthesize macroscopic materials where the likelihood of impurity inclusion escalates and, more importantly, to access molecular-to-nanoscopic-to-microscopic-to-macroscopic hierarchies, since the types and compositions of building blocks vary at each stage. Inspired by biological blends and high-entropy alloys, we hypothesize that diversifying the blend's composition can overcome these limitations. Increasing the number of components increases mixing entropy, leading to the dispersion of different components and, as a result, enhances interphase miscibility, weakens the dependence on specific pair interactions, and enables long-range cooperativity. This hypothesis is validated in complex blends containing small molecules, block copolymer-based supramolecules, and nanoparticles/colloidal particles. Hierarchically structured composites can be obtained with formulation flexibility in the filler selection and blend composition. It is worth noting that, by adding small molecules, we can solve the size constraint that plagues traditional block copolymer/nanoparticle blends. Detailed characterization and simulation further confirm that each component is distributed to locally mediate unfavorable interactions, cooperatively mitigate composition fluctuations, and retain structural fidelity. Furthermore, the blends have sufficient mobility to access tunable microstructures without compromising the order of the nanostructure. Besides establishing a kinetically viable pathway to release current constraints in the composite design and to navigate uncertainties during structure formation over multiple length scales, the present study demonstrates that entropy-driven behaviors can be realized in systems beyond high-entropy alloys despite inherent differences between metal alloys and organic/inorganic hybrids.

We have constructed photonic crystals (PCs) of a standard honeycomb lattice composed of solid dielectric columns, hollow dielectric columns, and composite dielectric columns and studied the influence of their dielectric constant and filling ratio on the topological boundary states. The optical quantum spin Hall effect is realized by compressing and stretching the standard honeycomb lattice. In the waveguide structure with sharp bends, cavity, and disorder, the electromagnetic (EM) wave is transmitted unidirectionally and robustly, which verifies the transmission characteristics of the topological edge states. In addition, by replacing several solid dielectric columns near the junction of PCs with different topological states with composite dielectric columns, disturbance is introduced to the edge states, and the influence of the relative effective permittivity of the composite dielectric columns on the edge states is studied. It is found that the EM wave in the gap between the upper boundary state and the lower boundary state cannot be transmitted, and with the increase of the relative effective permittivity of the composite dielectric columns, the gap becomes larger and larger, and the position of the gap gradually moves down. Based on this, a photonic crystal (PC) waveguide structure that has higher transmission efficiency, robust unidirectionality, and higher optical localization performance, is designed. It has more potential development in filters, optical switches, optical communication systems, and semiconductor technology.

The synthesis of photocatalysts with high charge separation and transfer efficiency are of immense significance in the process of using photocatalysis technology for wastewater treatment. In this study CdS/g-C 3 N 4 photocatalyst presented an improved morphology in its characterization using techniques such as SEM, DRS, PL, MS, EIS, and XRD, and enhanced photodegradation of oxcarbazepine. Different composites were obtained as confirmed by the various characterization techniques studied, including CdS/g-C 3 N 4 photocatalyst. The synthesized photocatalysts showed high visible light absorption efficiency within a range of ~655 to 420 nm. S-Scheme CdS/g-C 3 N 4 photocatalyst demonstrated high photocatalytic activity ascribed to high load separation and transition as shown in PL, Photocurrent reaction and EIS. It is understandable that CdS/g-C 3 N 4 photocatalyst have confirmed to be one of the ultimate promising entrants for groundbreaking photocatalyst scheming.

The proportional hazards (PH) assumption is the key assumption which may need to be examined in each survival analysis. It is the underlying assumption for the Cox proportional hazards and the log-rank test achieves its maximum efficiency when the PH assumption is satisfied. However, when the PH assumption is violated, we may not be able to provide a valid clinical interpretation for the hazard ratio of treatment effect, and the log-rank test may no longer achieve its desired level of power. Many alternative tests and measures have been developed for the non-proportional hazards situation. Four of them, Weighted log-rank test, Max-Combo Test (MX), Maximin Efficiency Robust Test (MERT) and The Restricted Mean Survival Time (RMST), are studied in this dissertation. Since previous papers only introduced MERT results by using uncensored case correlation matrix, MERT result with real censored correlation is discussed in this dissertation. The performance of the four non-proportional approaches, namely, Weighted log-rank test, MX, MERT, and RMST, is evaluated under the null and six typical proportional/non-proportional hazards conditions. The strength and weakness for each approach is explored in this dissertation. In addition, this proposal compares the test performance between Fleming-Harrington family G0,0, G1,0, G0,1, G1,1 and family G0,0, G2,0, G0,2, G2,2 for Weighted log-rank test, MX and MERT. The best non-proportional hazards test among those four tests and two families is explored in this dissertation. In clinical trials, two stage design is commonly used to dismiss ineffective treatment early at the end of the first stage, in order to avoid the high cost and long trial duration. Conditional power is the conditional probability of a significant result at the end of the trial given the data observed thus far. It is commonly used to evaluate the possibility of stopping the trial for futility. It also can be used to calculate the new sample size in the sample size re-estimation at the interim stage. The RMST is a robust measure of the survival time distribution. It provide a clinically interpretable summary and is widely used in the non-proportional hazards situation, since it does not rely on the PH assumption. This dissertation describes how to calculate the CP for the RMST endpoint at the interim stage for non-proportional hazards models. An approach for predicting survival curve at the final stage is developed in order to calculate the correlation in test statistics between the interim and final stages.

The intensity of emerging pollutants such as pharmaceuticals and personal care products (PPCPs) in the aquatic and terrestrial environment is a major source of concern to researchers. The current conventional methods of wastewater treatment plants are considered not efficient enough in the complete removal of the recalcitrant contaminants from water. The use of modified transition metals in visible responsive synthesis to degrade PPCPs and other pollutants (organic and inorganic) is considered as a developing green chemistry and sustainable technology. Hence, this review presents the state-of-the-art discussion on the novel photodegradation of PPCPs, and antibacterial activities of transition metal-modified magnetite materials for wastewater treatment, and suggested directions for the future. Transition metal-modified magnetite nanostructured photocatalysis is identified as one of the best candidates employed in advanced oxidation processes (AOPs) for wastewater treatment and has been found to efficiently destroy bacterial spores and effectively remove recalcitrant pollutants in water. Therefore, this article hopes to contribute scientific knowledge along with existing ones on advanced mechanisms and technology used in wastewater treatment.

Electrorheological (ER) valves have advantages of fast response speed and low energy loss. But, under the condition of high shear rates, the ER valves governed by traditional uniform electric field have poor performance and cannot meet the demands of applications with high speed loads. Existing researches show that when parallel components of an electric field were applied to the flow direction of ER fluids, the yield stress of the ER fluid can be greatly improved at high shear rates. Using non-uniform electric fields which can provide parallel components of electric field to the flow of ER fluids may make ER valves a possibility to meet the demands of working at high shear rates. In this paper, an intermittent staggered electrodes configuration was introduced, which can generate a non-uniform electric field with parallel components for ER valves. Distributions of electric fields are simulated and analyzed by COMSOL Multiphysics. An algorithm of the effective electric field strengths for non-uniform electric fields was introduced to evaluate the yield strength of the ER fluid. The ER valves' performances for applications at high shear rates can be assessed by the average values of effective electric field strengths in the working area of the electric field. The average values of effective electric field strengths varying with structural parameters of the intermittent staggered electrodes were studied. They have a peak value when varying with the increment of electrode widths, and rise up with increments of insulation widths and electrodes dislocation distances. The results provide a reference to the electrodes configuration design of ER valves governed by non-uniform electric field.

The refreshing rate of a multi-lines Braille display using electrorheological (ER) valves matrix plays a very important role to meet the demands of reading experiences of visual impaired people, a lower refreshing rate of Braille dots which is less than the reading rate of visual impaired people will stop them from using the Braille display and let them learn knowledge by listening. The refreshing rate is governed by the rate of flow of an ER valve which was used to be an actuator of the corresponding Braille dot. A mathematical model of the refreshing rate was established to learn the effects of the critical parameters of the ER valve on the rate of flow of the ER valve which is equivalent to the refreshing rate of the Braille display in this paper. The results show that to meet the demand of refreshing rate for visual impaired people, the governed voltages of ER valves should be higher than 1kV. The minimum value of operational governed voltages of an ER valve will decrease when higher tolerances were exploited to the parameters of channel of an ER valve. These results may provide some suggestions to design of an ER valve.

Background: In this article, the TR08 car of the Shanghai Magnetic Train Demonstration Line was prototyped and a multi-body dynamics simulation model was established. And based on the low-interference track irregularity power spectrum in Germany, track irregularity data was obtained. Used dynamic simulation software, completed the dynamic simulation analysis of the vehicle-rail model controlled by the proportion-integral-derivative control system PID parameters. It can be concluded that the vibration of trains passing through irregular tracks at different speeds, and evaluated its comfort. The optimal solution for the control of the PID parameters of the train also has been derived. Aim: Evaluation of operational comfort and suspension gap control effect of Shanghai Maglev Train Demonstration Line by simulation analysis. Materials and methods of the studies: Simulation analysis. Results: The vibration acceleration and suspension gap of Shanghai Maglev Train Demonstration Line has been obtained. Conclusion: By adjusting the parameters of PID control system, the vibration acceleration of train can be reduced and the ride comfort can be improved.

We propose a topological photonic crystal (PC) with split hexagonal ring structure by removing six isosceles trapezoids on the ring. By changing the size of trapezoid and hexagonal ring, we realize Dirac point and multi topology transition of the quadruple accidental degenerate. We simulate the quantum spin Hall effect (QSHE) and find that the EM wave (from 149.9 THz to 155.96 THz) almost achieves lossless transmission in the system, and is immune to sharp bends, cavity and disorder. At the junction of trivial and nontrivial photonic crystals (PCs), the topological trivial is replaced with the ordinary honeycomb lattice to construct line defect. We prove that the line defect has a non-spin-mixing defect mode with topological protection. The PC with line defect mode has high transmission efficiency, robust unidirectionality, and high optical local performance, which can not only be used in lasers, all-optical integrated circuits, optical communication systems and semiconductor technologies, but also will enrich the exploration of topological physics.

Paenibacillus elgii B69 produces a new xylose-containing exopolysaccharide (EPS) that effectively removes the pollutants from wastewater through flocculation. However, information about the biosynthesis of this EPS is limited. In this study, sequence analysis showed six putative glycosyltransferases (GTs) genes in polysaccharide gene clusters involved in glycosidic linkages of repeating units. Each gene was deleted and phenotypes were examined to understand the functions of these genes. Two of the genes were deleted successfully to encode a priming glucose GT and a side-chain xylose GT, but other genes were unsuccessfully deleted because of the accumulation of toxic intermediate products. The six genes were cloned and expressed in Escherichia coli, and the corresponding enzymes were purified. The activity of GTs was analyzed through mass spectrometry by using the purified membrane fraction as a lipid carrier receptor after a hexasaccharide repeated unit was reconstructed in vitro. The specificities of six different GTs and the building order of the hexasaccharide were characterized. This study provided a basis for future research on the biosynthetic pathway of EPS in Paenibacillus or other genera.

The intensity of emerging pollutants such as pharmaceuticals and personal care products (PPCPs) in the aquatic and terrestrial environment is a major source of concern to researchers. The current conventional methods of wastewater treatment plants are considered not efficient enough in the complete removal of the recalcitrant contaminants from water. The use of modified transition metals in visible responsive synthesis to degrade PPCPs and other pollutants (organic and inorganic) is considered as a developing green chemistry and sustainable technology. Hence, this review presents the state-of-the-art discussion on the novel photodegradation of PPCPs, and antibacterial activities of transition metal-modified magnetite materials for wastewater treatment, and suggested directions for the future. Transition metal-modified magnetite nanostructured photocatalysis is identified as one of the best candidates employed in advanced oxidation processes (AOPs) for wastewater treatment and has been found to efficiently destroy bacterial spores and effectively remove recalcitrant pollutants in water. Therefore, this article hopes to contribute scientific knowledge along with existing ones on advanced mechanisms and technology used in wastewater treatment.

The objective of the current work is to shed light on studying the air flow features of the air path which is part of the passive containment cooling system (PCS) in a pressurized water reactor design. A wind tunnel test using a 1:100 scaled model is established to study the characteristic called “wind-neutrality” of the air flow in the air path, which indicates that the environmental wind should not be beneficial or detrimental to the air flow for containment cooling. Test results show that the pressure distribution in the air path is uniform, and wind speeds, wind angles, and surroundings have little effect on air flow uniformity. These investigations show that it is possible to understand air flows in the air path of PCS with a scale wind tunnel test.

In this paper, the flow field of the approximate T-shaped tundish and the removal rate of fine inclusions are improved by changing the parameters of the flow control device of the SCB (stabilizer coupling baffle) structure. Studies have shown that the synergistic effect of the DPRW (double porous retaining wall) structure and the IRS (internal rotation stabilizer) structure has excellent performance in mixing the temperature composition of the molten steel, increasing the average residence time of the molten steel, reducing the volume fraction of the dead zone, and improving the removal rate of fine inclusions. The opening method and diameter of the double-layer retaining wall have a greater impact on the flow field parameters. The larger the diameter, the more conducive to increasing the average residence time, and the smaller the diameter, the more conducive to increasing the removal rate of fine inclusions.

The original publication of the article contained an incorrect reference citation in “Results” section. The corrected text has been given below.

In this paper, we study the stochastic heat equation with a general multiplicative Gaussian noise that is white in time and colored in space. Both regularity and strict positivity of the densities of the solution have been established. The difficulty, and hence the contribution, of the paper lie in three aspects, which include rough initial conditions, degenerate diffusion coefficient, and weakest possible assumptions on the correlation function of the noise. In particular, our results cover the parabolic Anderson model starting from a Dirac delta initial measure., Comment: 94 pages

High-speed maglev, as the fastest transportation on the ground, may become the most promising long-distance transportation choice in the future. The dynamic characteristics of the girder, which is the main supporting member, is very important to the design and health monitoring of the maglev transportation system. This paper presents the field measurement and numerical analysis of the dynamic behavior of the guideway girders in Shanghai high-speed maglev test line. An output-only time-domain system identification method namely, the Natural Excitation Technique (NExT) coupled with the Eigensystem Realization Algorithm (ERA) was used in this study. The dynamic responses of the girders are presented and analyzed in both time and frequency domains. The results show that the NExT-ERA method can well predict the inherent dynamic properties of the girders.

As a large scale passive pressurized water reactor nuclear power plant, CAP1400 can remove the reactor decay heat to outside containment with the air cooling in the air flow path of passive containment cooling system (PCS) during the long-term period following an accident. Flow resistance characteristic and wind neutrality characteristic are the main performances of PCS air flow path. In order to study the performance of PCS air flow path, it is necessary to carry out the PCS wind tunnel test and computational fluid dynamics (CFD) analysis to establish a suitable method for the analysis of the performance of the air flow path. This paper comes up simulating the internal pressure and velocity distribution in the air flow path under different wind speed through CAP1400 PCS 1:100 scaled air flow path wind tunnel test to research the air flow resistance and internal flow pattern. The test shows that local uneven flow phenomenon exists in the outer annulus of the air flow path, but the wind pressure distribution of inner annulus is not affected by environment wind speed, wind direction angle, landforms and the surrounding buildings. The wind pressure is uniform at different heights on the cross section and shows the neutrality feature. Combining with CAP1400 PCS wind tunnel test, the CFD model is built. The measured inlet wind speed, turbulent kinetic energy and turbulent dissipation rate distribution parameters are inputs and the uniform wind conditions and gradient wind conditions of simulation analysis are developed. Simulation results show that: 1) In uniform wind condition, simulation result of pressure coefficient distribution trend at each cross section is consistent with the test trend and the deviation is very small, which basically can be controlled below 5%. The simulated differential pressures between inner annulus and outer annulus at different elevation are basically identical with the test results, which increase as the elevation arises. The simulated velocity distribution is basically identical with the test. The wind velocity at the upwind and central area of the flow path outlet is larger than other area, and a large swirling region comes on the leeward side near the wall 15cm, but simulated swirling region size at leeward side is slightly smaller. 2) In gradient wind condition, the pressure coefficient distribution trends are basically identical, and the deviation between the test and CFD analysis is 5–10% approximately. Considering the stability of gradient wind condition in wind tunnel is worse than that of uniform wind conditions, and more prone to wind speed fluctuations, therefore, the deviation is slightly greater than the uniform wind condition. According to the CFD simulation and wind tunnel test, it can be found that the simulation of air flow inside and outside annulus has a high precision though the test results are slightly affected by the instrument tubes along the two sides of test model. In general, CFD simulation and wind tunnel test results are basically identical. Therefore, CFD analysis method is well verified by PCS wind tunnel test, which can be applied to the analysis of the actual power plant.

CAP1400 is a large passive pressurized water reactor nuclear power plant, which relies on engineering safety features such as passive containment cooling system (PCS) to remove the decay heat in the containment and mitigate accident consequences. PCS is designed to perform passive containment cooling which is mainly dependent on natural convection inside the containment and inner wall condensation heat transfer, outer containment surface water film coverage and evaporation heat transfer and external air flow path cooling performance, etc. Among them, the key factors that affect the performance of the external air flow path include the flow resistance characteristics of the air flow path and the wind-direction neutrality characteristics. The relevant performance will be the important design input of the accident analysis, which will directly affect the safety of the power plant. During the normal operation of power plant, the PCS air flow path is influenced by the external environment, and its internal flow is very complicated. Designers are often lack of data support, and can’t fully consider the impact of environmental flow. In order to fully study the performance of PCS air flow path, it is necessary to perform PCS integrated scaled wind tunnel test. According to the original design of CAP1400 PCS system, the model scale research is developed and CAP1400 PCS wind tunnel test scaled model is established and the scale is 1:100. The test model includes shield building model and the surrounding plant model, which contain pressure measuring points uniformly distributed in 6 horizontal cross sections of the shield building. The pressure measuring point arrangement does not affect air flow in the air flow path. The following wind tunnel tests are simulated in different wind speed including 15m/s, 20m/s, 10m/s, 25m/s. The air flow pressure, wind velocity at the inlet and outlet of air flow path and the pressure distribution of inner annulus and outer annulus are measured in order to study the air flow pressure drop and wind-direction neutrality characteristics, and the wind tunnel test also considers the different wind direction angle, with and without the surrounding buildings and the effects of different landforms. The test results show that the flow rate of inlet and outlet of air flow path is balanced and the wind velocity at the upwind and central area of the flow path outlet is larger than other area, and a large vortex comes on the leeward side near the wall. The local uneven flow phenomenon exists in the outer annulus of the air flow path, but the wind pressure distribution of inner annulus is not affected by environment wind speed, wind direction angle, landforms and the surrounding buildings. So CAP1400 PCS air flow path has the characteristics of wind direction neutrality, and the natural convection of the air flow path will not be adversely affected by the environment wind.

The tri-functional purpose of Microbial Desalination Cell (MDC) has shown a great promise in our current scarcity of water, an increase in water pollution and the high cost of electricity production. As a biological system, the baseline force that drives its performance is the presence of exoelectrogens in the anode chamber. Their presence in the anodic chamber of MDC systems enables the treatment of water, desalination of seawater, and the production of electrical energy. This study reviews the characteristics of exoelectrogens, as a driving force in MDC and examines factors which influence their growth and the performance efficiency of MDC systems. It also addresses the efficiency of mixed cultures with certain predominant species as compared to pure cultures used in MDC systems. Furthermore, the study suggests the need to genetically modify certain predominant strains in mixed cultures to enhance their performance in COD removal, desalination and power output and the integration of MDC with other technologies for cost-effective processes.

We investigate the growth of the tallest peaks of random field solutions to the parabolic Anderson models over concentric balls as the radii approach infinity. The noise is white in time and correlated in space. The spatial correlation function is either bounded or non-negative satisfying Dalang's condition. The initial data are Borel measures with compact supports, in particular, include Dirac masses. The results obtained are related to those of Conus, Joseph and Khoshnevisan 2013 and X. Chen 2016, where constant initial data are considered.

The responses of soil enzyme activity of freshwater marsh, microbial biomass carbon (MBC), dissolved organic carbon (DOC) and aboveground biomass to water gradients were studied with Carex lasiocarpa pot culture experiment. The relationships between soil enzyme activity and MBC, DOC and aboveground biomass were discussed. The water gradients were W1, 15 cm; W2, −5 cm; W3, −5–5 cm; W4, submerged. The results indicated that acid phosphatase, invertase and urease activities were decreased with the increase of water level, while catalase activity was increased with moisture content increasing. Drying-wetting alternation (W3) increased soil enzyme activities if compared with W1. MBC content followed the order of W3 > W1 > W2 > W4, and the activities of invertase, urease and catalase were significantly positively correlated with MBC (p W1 > W3 > W2, and the activities of urease and acid phosphatase were most significantly negatively correlated with DOC (p < 0.01). In addition, drying-wetting alternation promoted the growth of Carex lasiocarpa. When water submerged plants, the growth of Carex lasiocarpa was significantly inhibited. The aboveground biomass was positively related to soil enzyme activities. There were close relationships between the activities of invertase, urease and catalase and the growth situation of Carex lasiocarpa.

In the last few decades, rectangle earth pressure balance shield machine have been introduced as primary tunneling tools in soft soil excavation around the world. This paper presents research on the performance of the rectangle shield machine. Analytical studies have been carried out to establish the relation between rectangle shield machine design key parameters, such as segments support, tail thickness and soil layer harness, and the strength, stiffness and buckling analysis of the shell structure. The results of these are presented. And the results show that good stiffness, displacement and stability capacities have been achieved.

In this paper, we study the stochastic wave equations in the spatial dimension 3 driven by a Gaussian noise which is white in time and correlated in space. Our main concern is the sample path H��lder continuity of the solution both in time variable and in space variables. The conditions are given either in terms of the mean H��lder continuity of the covariance function or in terms of its spectral measure. Some examples of the covariance functions are proved to satisfy our conditions, which include the case of the work \cite{dalang4}. In particular, we obtain the H��lder continuity results for the solution of the stochastic wave equations driven by (space inhomogeneous) fractional Brownian noises. For this particular noise, the optimality of the obtained H��lder exponents is also discussed., 40 pages

In MFCW (multi-frequency continuous-wave) systems, sidetones are generally transmitted by angular modulation. A novel method named SLP (spectrum-line processing) for analyzing the phase shift of the demodulated sidetone of the distorted monotone FM signal after passing a linear system is presented firstly, and then generalized to nonlinear systems. Compared to the complicated traditional method, the effect of nonideal channel characteristics on the demodulated sidetone phase when frequency or power of the carrier varies can be effectively analyzed.

High performance and low cost RF data transmitters and receivers suitable for home and building applications are reported. The principal design guidelines for transmitters and receivers in such applications are introduced. A remote meter reading system is illustrated to demonstrate their typical application.

A digital distance simulator is developed to fulfil static accuracy test for a multi-frequency continuous-wave (MFCW) ranging system. The Baseband Phase Shift Simulation Method is presented to solve the conflict between high resolution and long range. With the adoption of the Direct Digital Synthesizer (DDS), the simulator can achieve the relative resolution of 0.015% with low complexity and high flexibility.

A novel narrow-bandwidth, multi-frequency continuous-wave (MFCW) ranging system to measure the distance of a weather balloon is introduced. Compared to the pulsed system, it has advantages of high accuracy, strong noise-rejection ability, narrow bandwidth and low cost. The key points in the system and test results are presented.