A multiplicity result for a class of elliptic boundary value problems

We consider a mildly nonlinear elliptic boundary value problem depending on a parameter. Given appropriate hypotheses concerning the asymptotic behaviour of the nonlinearity, we derive lower bounds on the number of solutions. The results complement an earlier theorem due to Kazdan and Warner [6

A multiplicity result for a class of elliptic boundary value problems

SynopsisWe consider a mildly nonlinear elliptic boundary value problem depending on a parameter. Given appropriate hypotheses concerning the asymptotic behaviour of the nonlinearity, we derive lower bounds on the number of solutions. The results complement an earlier theorem due to Kazdan and Warner [6]

Low voltage to high voltage level shifter and related methods

A shifter circuit comprises a high and low voltage buffer stages and an output buffer stage. The high voltage buffer stage comprises multiple transistors arranged in a transistor stack having a plurality of intermediate nodes connecting individual transistors along the stack. The transistor stack is connected between a voltage level being shifted to and an input voltage. An inverter of this stage comprises multiple inputs and an output. Inverter inputs are connected to a respective intermediate node of the transistor stack. The low voltage buffer stage has an input connected to the input voltage and an output, and is operably connected to the high voltage buffer stage. The low voltage buffer stage is connected between a voltage level being shifted away from and a lower voltage. The output buffer stage is driven by the outputs of the high voltage buffer stage inverter and the low voltage buffer stage

Montana's Crucial Areas and Connectivity Assessment: An Update and Demonstration of the Crucial Areas Mapping Service

Montana Fish, Wildlife and Parks (FWP) completed the Comprehensive Fish and Wildlife Conservation Strategy (CFWCS) in October 2005 as a landscape level plan to identify aquatic and terrestrial focus areas important to species and habitats of "Greatest Conservation Need." As implementation of the CFWCS began, FWP saw a need to refine the conservation scale and include terrestrial game and sport fish, FWP lands, and other recreational values into a Comprehensive Plan for Conservation. The "Crucial Areas and Connectivity Assessment" is an attempt to refine the conservation scale and identify important game and nongame fish and wildlife habitats, critical corridors, and valued recreational areas using a combination of empirical data, modeling based on these data, and expert opinion. The goal of this project is to identify and display critical and important habitats for fish and wildlife. Multiple benefits are perceived through achievement of this goal: increased efficiency in planning and commenting on development proposals, effective targeting and planning for the conservation of valued habitats, and increased opportunity for coordination with other agencies states. FWP spent the past year developing data layers, vetting the layers both internally and within the scientific community. Layers available to date include: game quality, game fish life history, watershed integrity, species of concern, aquatic connectivity, angler use, terrestrial species richness, and core area index. In parallel, FWP has developed an interactive Crucial Areas Mapping Service (CAMS) that depicts these resource values and allows users to relate each resource value to risk factors including energy development, urbanization, and subdivision. As the project develops and nears completion, best management practices and policy related to critical habitats will be produced. In mid-March, we plan to release CAMS to the public as a preplanning tool and comprehensive decision support system

Electronic Switch Arrays for Managing Microbattery Arrays

Integrated circuits have been invented for managing the charging and discharging of such advanced miniature energy-storage devices as planar arrays of microscopic energy-storage elements [typically, microscopic electrochemical cells (microbatteries) or microcapacitors]. The architecture of these circuits enables implementation of the following energy-management options: dynamic configuration of the elements of an array into a series or parallel combination of banks (subarrarys), each array comprising a series of parallel combination of elements; direct addressing of individual banks for charging/or discharging; and, disconnection of defective elements and corresponding reconfiguration of the rest of the array to utilize the remaining functional elements to obtain the desited voltage and current performance. An integrated circuit according to the invention consists partly of a planar array of field-effect transistors that function as switches for routing electric power among the energy-storage elements, the power source, and the load. To connect the energy-storage elements to the power source for charging, a specific subset of switches is closed; to connect the energy-storage elements to the load for discharging, a different specific set of switches is closed. Also included in the integrated circuit is circuitry for monitoring and controlling charging and discharging. The control and monitoring circuitry, the switching transistors, and interconnecting metal lines are laid out on the integrated-circuit chip in a pattern that registers with the array of energy-storage elements. There is a design option to either (1) fabricate the energy-storage elements in the corresponding locations on, and as an integral part of, this integrated circuit; or (2) following a flip-chip approach, fabricate the array of energy-storage elements on a separate integrated-circuit chip and then align and bond the two chips together

Analysis of silica-supported vanadia by X-ray absorption spectroscopy: Combined theoretical and experimental studies

In this study we combine density-functional theory (DFT) calculations on oxygen core excitations in vanadia-silica model clusters with in situ X-ray absorption fine structure (NEXAFS) measurements near the oxygen K-edge of vanadia model catalysts supported by silica SBA-15 in order to analyze structural details of the vanadia species. The silica support is found to contribute to the NEXAFS spectrum in an energy range well above that of the vanadium oxide units allowing a clear separation between the corresponding contributions. Further, differently coordinated oxygen which is characteristic for particular vanadia species, monomeric or non-monomeric, can be identified in the theoretical spectra consistent with the oxygen K-edge NEXAFS measurements. The comparison of the theoretical and experimental NEXAFS spectra provides clear evidence that under in situ conditions different molecular vanadia species, in particular non-monomeric VxOy, exist at the catalyst surface and the exclusive presence of monomeric vanadia groups can be ruled out. The present analysis goes beyond earlier work applying vibrational spectroscopy to the present systems where, as a result of extended vibrational coupling, a separation between vanadia, silica, and interface contributions was less successful

Structural characterization of vanadium oxide catalysts supported on nanostructured silica SBA-15 using X-ray absorption spectroscopy

The local structure of vanadium oxide supported on nanostructured SiO2 (VxOy/SBA-15) was investigated by in situ X-ray absorption spectroscopy (XAS). Because the number of potential parameters in XAS data analysis often exceeds the number of "independent" parameters, evaluating the reliability and significance of a particular fitting procedure is mandatory. The number of independent parameters (Nyquist) may not be sufficient. Hence, in addition to the number of independent parameters, a novel approach to evaluate the significance of structural fitting parameters in XAS data analysis is introduced. Three samples with different V loadings (i.e. 2.7 wt %, 5.4 wt %, and 10.8 wt %) were employed. Thermal treatment in air at 623 K resulted in characteristic structural changes of the V oxide species. Independent of the V loading, the local structure around V centers in dehydrated VxOy/SBA-15 corresponded to an ordered arrangement of adjacent V2O7 units. Moreover, the V2O7 units were found to persist under selective oxidation reaction conditions