A Spectral Gap Estimate and Applications

We consider the Schr\"odinger operator -\frac{d^2}{d x^2} + V \qquad \mbox{on an interval}~~[a,b]~\mbox{with Dirichlet boundary conditions}, where $V$ is bounded from below and prove a lower bound on the first eigenvalue $\lambda_1$ in terms of sublevel estimates: if $w_V(y) = |I_y|,\text{ where } I_y := \left\{ x \in [a,b]: V(x) \leq y \right\},$ then $$\lambda_1 \geq \frac{1}{250} \min_{y > \min V}{\left(\frac{1}{w_V(y)^2} + y\right)}.$$ The result is sharp up to a universal constant if $\left\{ x \in [a,b]: V(x) \leq y \right\}$ is an interval for the value of $y$ solving the minimization problem. An immediate application is as follows: let $\Omega \subset \mathbb{R}^2$ be a convex domain with inradius $\rho$ and diameter $D$ and let $u:\Omega \rightarrow \mathbb{R}$ be the first eigenfunction of the Laplacian $-\Delta$ on $\Omega$ with Dirichlet boundary conditions on $\partial \Omega$. We prove $$\| u \|_{L^{\infty}} \lesssim \frac{1}{\rho^{}} \left( \frac{\rho}{D} \right)^{1/6} \|u\|_{L^2},$$ which answers a question of van den Berg in the special case of two dimensions

Object partitioning considered harmful : space subdivision for BVHs

A major factor for the efficiency of ray tracing is the use of good acceleration structures. Recently, bounding volume hierarchies (BVHs) have become the preferred acceleration structures, due to their competitive performance and greater flexibility compared to KD trees. In this paper, we present a study on algorithms for the construction of optimal BVHs. Due to the exponential nature of the problem, constructing optimal BVHs for ray tracing remains an open topic. By exploiting the linearity of the surface area heuristic (SAH), we develop an algorithm that can find optimal partitions in polynomial time. We further generalize this algorithm and show that every SAH-based KD tree or BVH construction algorithm is a special case of the generic algorithm. Based on a number of experiments with the generic algorithm, we conclude that the assumption of non-terminating rays in the surface area cost model becomes a major obstacle for using the full potential of BVHs. We also observe that enforcing space subdivision helps to improve BVH performance. Finally, we develop a simple space partitioning algorithm for building efficient BVHs

Reliability Prediction of Thick Film Hybrid Integrated Circuits

When using the well known handbooks for reliability predicting (MIL, CNET) some problems occur in quality assessment of components which are not produced according to the requirements of the US military or the French standards. The results obtained from tests of Test Pattern Circuits may be used successfully for reliability estimating during the design period of new thick film Hybrid Integrated Circuits. Six types of Test Pattern Circuits were designed and tested and a model for estimating thick film Hybrid Integrated Circuits failure rate is proposed. Failure rate values predicted by using the method with Test Pattern Circuits, and the results, obtained from the tests of two kinds of Hybrid Integrated Circuits concerned for a 90% confidence level were compared

Five-year follow-up of implants placed simultaneously with inferior alveolar nerve lateralisation or transposition

Introduction: The aim of this investigation was to evaluate the 5-year outcomes regarding presence of intraoperative and postoperative complications and the survival rate of implants placed simultaneously with lower alveolar nerve lateralization or transposition.Material and Methods: implants placement was performed on 34 patients with advanced atrophy of the posterior mandible simultaneously with lower alveolar nerve lateralization or transposition. Transposition was done only in two cases; in the rest of the cases lateralization of lower alveolar nerve was performed.Results: The survival rate at the end of the fifth year after implant placement was 100%. The mean height of residual bone at the region of implant placement was 2.76 mm. The mean marginal bone resorption for at the fifth year was 0.309 mm. In 20.6% of cases a positive BOP (bleeding on probing) was registered. 14.7% of the patients were free of symptoms of NSD (neuro-sensory dysfunction). In the rest of the patients the mean duration of NSD was 2.06 weeks. In 76.4% of patients the symptoms of NSD of nervus alveolaris inf. resolved after the second week. The maximum period of reported NSD was 6 weeks. No permanent NSD occured.Conclusion: Properly performed lateralization or transposition of the lower alveolar nerve is associated with minimal risk of permanent neuro-sensory dysfunction and providing an opportunity for placement of intraosseal implants in the posterior mandible with high survival rate

Xenon inhibits excitatory but not inhibitory transmission in rat spinal cord dorsal horn neurons

<p>Abstract</p> <p>Background</p> <p>The molecular targets for the promising gaseous anaesthetic xenon are still under investigation. Most studies identify <it>N</it>-methyl-D-aspartate (NMDA) receptors as the primary molecular target for xenon, but the role of α-amino-3-hydroxy-5-methyl-4-isoxazole-4-propionic acid (AMPA) receptors is less clear. In this study we evaluated the effect of xenon on excitatory and inhibitory synaptic transmission in the superficial dorsal horn of the spinal cord using <it>in vitro </it>patch-clamp recordings from rat spinal cord slices. We further evaluated the effects of xenon on innocuous and noxious stimuli using <it>in vivo </it>patch-clamp method.</p> <p>Results</p> <p><it>In vitro</it>, xenon decreased the amplitude and area under the curve of currents induced by exogenous NMDA and AMPA and inhibited dorsal root stimulation-evoked excitatory postsynaptic currents. Xenon decreased the amplitude, but not the frequency, of miniature excitatory postsynaptic currents. There was no discernible effect on miniature or evoked inhibitory postsynaptic currents or on the current induced by inhibitory neurotransmitters. <it>In vivo</it>, xenon inhibited responses to tactile and painful stimuli even in the presence of NMDA receptor antagonist.</p> <p>Conclusions</p> <p>Xenon inhibits glutamatergic excitatory transmission in the superficial dorsal horn <it>via </it>a postsynaptic mechanism. There is no substantial effect on inhibitory synaptic transmission at the concentration we used. The blunting of excitation in the dorsal horn lamina II neurons could underlie the analgesic effect of xenon.</p

Long-term follow-up of implants with reduced length

Introduction: The aim of this study was to assess the reduced length implants as an alternative of conventional length implants in combination with bone augmentation. The following criteria were observed: survival rate, marginal bone loss, bleeding on probing.Material and Methods: This study included 186 Straumann Standard Plus implants with dimensions: length of 6 mm and diameter of 4.8 mm. The implants were loaded with non-removable crowns or bridges at least 10 weeks after the implant placement. Depending on the type of the prosthetic option the distribution of the implants was as follows: 83 implants were co-abutments to one more implant with conventional length (8-14 mm); 67 implants were co-abutments to more than one implant with conventional length, 33 implants were loaded with single crowns.Results: The mean period of observation was 5.59 years. The mean marginal bone resorption was 0,224mm. In 12.4% from the cases was registered BOP (bleeding on probing). A correlation was found between the BOP and mean marginal bone resorption. No correlation was found between the values of marginal bone resorption and the type of the prosthetics. The survival rate of the implants in the observation period was 99.5%.Conclusion: Тreatment by short implants is a reliable alternative to implants with conventional length with combination of bone grafting procedures. It is less invasive, cost effective and consumes less treatment time

A Linear Complementarity Numerical Approach to the Non-Convex Problem of Structures Environmentally Damaged and Strengthened by Cable-Bracings

A computational treatment is presented for the mathematically rigorous analysis of civil engineering structures, which have been environmentally damaged and subsequently strengthened by cable-elements. The problem is treated as an inequality one, where the governing conditions are equalities as well as inequalities. The cable behavior is considered as nonconvex and nonmonotone one and is described by generalized subdifferential relations including loosening, elastoplastic - fracturing and other effects. Using piece-wise linearization for the cable behavior, a linear complementarity problem, with a reduced number of unknowns, is solved by optimization algorithms. Finally, an example from Civil and Environmental Engineering praxis is presented

Diagnosis and treatment of enterovesical fistulas

A fistula is an atypical connection between two epithelial surface. We studied retrospectively four male pa­tients with enterovesical fistulas treated in our departments between March 2016 - March 2017. These in­cluded colovesical, rectovesical and ileovesical fistulas. Patients presented with urinary symptoms (pneu­maturia, faecaluria and recurrent urinary tract infections). One patient had received radiotherapy after rec­tal resection for rectal carcinoma. For another of the cases the fistula was being due to periprostatic abscess. The third patient was diagnosed with bladder carcinoma with rectal invasion. The fourth patient was with direct invasion of sigmoid cancer to the bladder. The most common investigations included abdominal ul­trasound, CT scan, cystoscopy and colonoscopy. Enteral stoma was performed in all cases as a part of sur­gical treatment.All patients underwent open procedure, as a main rule enteral stoma was performed to cease the contami­nation, and primary repair of the bladder was performed. No recurrences were recorded, but there were sev­eral complications, including Clavien-Dindo gr. V. Most of the complications were treated by interventional urology. In conlusion, enteral division and primary repair of the bladder are safe approaches for treatment of enterovesical fistulas. As a rule ceasing of contamination should always be performed. Cystoscopy can manage most of the complications occurring in the early postoperative period. Scr Sci Med 2017; 49(3): 53-5

Comparison of the rates of bone regeneration in sinus lift grafting with a calcium-phosphate paste between the 6th and the 9th month - a clinical case

Maxillary sinus floor augmentation has been used for occlusal rehabilitation with prosthetic appliances installed over dental implants in the posterior maxilla despite the fact that this region often presents loss of alveolar bone and increased maxillary sinus pneumatization, particularly when all of the molars are absent. The shortage and quality of the remaining bone often implies a challenge when rehabilitating with dental implants. Different kinds of grafts have been used in an endeavour to solve these problems. The aim of thisstudy is to find out if there is a significant difference in the bone formation between the 6th- and the 9th - month periods after sinus lift grafting with a calcium- phosphate paste (Maxresorb inj. (Botiss Dental, Berlin, Germany)). For this purpose a bilateral sinus lift has been made by own methodology. Results showed no significant difference in the percentage of newly formed bone in the sixth and the ninth month, which warrants the dental implants to be placed on the sixth month post-sinus lifting