On compact manifolds (M, g) without boundary of dimension n ≥ 2, the gradient estimates for unit band spectral projection operators χλ is proved for any second order elliptic differential operators L by maximum principle. A new proof of Hörmander Multiplier Theorem on the eigenfunction expansion of the operator L is given in this setting by using the gradient estimates and the Calderón-Zygmund ...

Approximate resolution of linear systems of differential equationswith varying coefficients is a recurrent problem, shared by a number of scientific and engineering areas, ranging from QuantumMechanics to Control Theory. When formulated in operator or matrix form, the Magnus expansion furnishes an elegant setting to build up approximate exponential representations of the solution of the system....

Tissue expansion is a popular technique in plastic and reconstructive surgery that grows skin in vivo for correction of large defects such as burns and giant congenital nevi. Despite its widespread use, planning and executing an expansion protocol is challenging due to the difficulty in measuring the deformation imposed at each inflation step and over the length of the procedure. Quantifying th...

OBJECTIVES To compare transverse skeletal changes produced by rapid (RME) and slow (SME) maxillary expansion using low-dose computed tomography. The null hypothesis was that SME and RME are equally effective in producing skeletal maxillary expansion in patients with posterior crossbite. SETTING AND SAMPLE POPULATION This study was carried out at the Department of Oral Sciences, University of ...

he previous articles in this issue have dealt in depth with the technique of tissue expansion and its unique and remarkable advantages for T soft tissue reconstruction. However, as with all aspects of cutaneous surgery, tissue expansion does have its share of disadvantages and potential complications (Table 1). The disadvantages of tissue expansion are relatively few. The procedure does require...

The dimensional changes of 4 types commercial luting cements after setting were examined in distilled water, using a developed thermal expansion testing apparatus. The measurements were carried out under three conditions: increasing temperature (from 37•Ž to 60•Ž), decreasing temperature (from 37•Ž to 10•Ž), and constant temperature (37•Ž). The results indicated that: (1) the zinc phosphate cem...

We built a filtering system YFILTER this year, which we used for experiments on profile updating and thresholds setting. Our focus is using incremental Rocchio for introducing new query terms and term weighting. Although 1, 0.5, 0.25 is a widely used Rocchio ratio for query expansion based on relevance feedback, we found that the optimal setting for information filtering is corpus and profile d...

INTRODUCTION Web query log is a type of file keeping track of the activities of the users who are utilizing a search engine. Compared to traditional information retrieval setting in which documents are the only information source available, query logs are an additional information source in the Web search setting. Based on query logs, a set of Web mining techniques, such as log-based query clus...

We show that the normal form of Taylor expansion a $\lambda$-term is isomorphic to its B\"ohm tree, improving Ehrhard and Regnier's original proof along three independent directions. First, we simplify final step by following left reduction strategy directly in resource calculus, avoiding introduce an abstract machine ad hoc. also groupoid permutations copies arguments rigid variant relate coef...

In this study, two improved dental stones were used to fabricate master casts and dies. The tested fabrications were BegoStone (Bego Bremer, Goldschlägerei Wilh. Herbst GmbH and Co. Wilhelm HerbstStrabe 1 D 28359 Bremen Germany), Moldano (Heraeus Kulzer GmbH and Co. KG Gruner Weg 11 D-63450 Hanau Germany) and plaster of paris (BMT, PK 121 Sivas, Turkey). Together with the manufacturer’s values,...