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We consider Artin-Tits groups of FC type and prove the two following results. If any two distinct elements of a standard parabolic subgroup are conjugated by a standard generator of the whole group, then this generator has to be in the subgroup. We also prove that classical transversals of standard parabolic subgroups of Artin-Tits groups of FC type are compatible with intersection with standard parabolic subgroups: If A X , A Y are two standard parabolic subgroups of an Artin-Tits groups A of FC type and T is the classical transversal of A X in A, then T ∩ A Y is a transversal of A X ∩ Y in A Y . So the two properties hold for Artin-Tits groups of spherical type and Right-angled Artin-Tits groups.

In this work, we define the hypersurfaces of the spherical type degenerated (in short DST-hypersurfaces), these hypersurfaces has the geometric property that the middle spheres pass through the origin of the Euclidean space. We present a representation for these hypersurfaces in the case where the stereographic projection of the Gauss map N is given by the identity application. We characterize the DST-hypersurfaces through a differential equation and we give an explicit example of a two-parameter family of DST-hypersurfaces with planar lines of curvature foliated by (n-1)-dimensional spheres. Moreover, we classify the DST hypersurfaces of rotation.

We give a conjectural classification of virtually cocompactly cubulated Artin–Tits groups (i.e., having a finite index subgroup acting geometrically on a CAT(0) cube complex), which we prove for all Artin–Tits groups of spherical type, FC type, or two-dimensional type. A particular case is that for $n \geqslant 4$, the $n$-strand braid group is not virtually cocompactly cubulated.

The effect of epoxy species on the tensile and electrical insulation properties of epoxy/micro-silica composites was studied by using three species of epoxy resins for high voltage insulators. The mixing ratio of spherical type micro-silica was varied at 40–70 wt% in each epoxy systems. Tensile strength of three Epoxy/micro-silica composites was lower than that of the each neat epoxy system and increased with increasing micro-silica content in each system. The maximum tensile strength was 86.0 MPa in Epoxy 2/micro-silica (70 wt%) composite. Electrical insulation breakdown strength of three Epoxy 1/micro-silica, Epoxy 2/micro-silica, Epoxy 3/micro-silica composites was higher than that of the each neat Epoxy 1, Epoxy 2 and Epoxy 3. The maximum electrical insulation breakdown strength was 55 kV/2mm in Epoxy 2/micro-silica (50 wt%) composite.

Artin–Tits groups act on a certain delta-hyperbolic complex, called the “additional length complex”. For an element of the group, acting loxodromically on this complex is a property analogous to the property of being pseudo-Anosov for elements of mapping class groups. By analogy with a well-known conjecture about mapping class groups, we conjecture that “most” elements of Artin–Tits groups act loxodromically. More precisely, in the Cayley graph of a subgroup G of an Artin–Tits group, the proportion of loxodromically acting elements in a ball of large radius should tend to one as the radius tends to infinity. In this paper, we give a condition guaranteeing that this proportion stays away from zero. This condition is satisfied e.g. for Artin–Tits groups of spherical type, their pure subgroups and some of their commutator subgroups.

espanolEm [2], foi obtida uma caracterizacao das superficies em R3 que sao envelopes de uma congruencia de esferas em R3, na qual o outro envelope esta em R2. Neste artigo, caracterizamos as superficies de H3 e S3 que sao envelopes de uma congruencia de esferas geodesicas em H3 e S3, respectivamente, na qual o outro envelope esta contido em H2 H3 e S2 S3. Mostramos que esta caracterizacao permite obter localmente uma parametrizacao das superficies contidas em H3 e S3, esta caracterizacao estende o resultado obtido em [2]. Alem disso, damos condicoes suficientes para que estas superficies estejam associadas localmente por uma transformacao de Ribaucour. Tambem, apresentamos familias de superficies parametrizadas por linhas de curvatura H3 e S3, que dependem unicamente de uma funcao de duas variaveis, a qual e solucao de uma equacao diferencial. Finalmente, caracterizamos as superficies de tipo esferico em H3 e S3, como as superficies onde sua funcao raio e solucao da equacao de Helmholtz. EnglishIn [2], was obtained a characterization of the surfaces in R3 which are envelopes of a sphere congruence in R3, in which the other envelope is in R2. In this paper, we characterize the surfaces of H3 and S3 which are envelopes of a congruence of geodesic spheres in H3 and S3, respectively, in which the other envelope is contained in H2 H3and S2 S3. We show that this characterization allows locally to obtain a parameterization of the surfaces contained in H3 and S3, this characterization extends the result obtained in [2]. Moreover, we provide sufficient conditions for these surfaces to be locally associated by a transformation of Ribaucour. Also, we present families of surfaces parameterized by lines of curvature in H3 and S3, which depend on a function of two variables which is solution of a differential equation. Finally, we characterize the surfaces of the spherical type in H3 and S3, as the surfaces where its radius function is the solution of the Helmholtz equation.

The geometrical arrangement and thermal insulation performance of the thermal insulation system are two of the most crucial issues for the design of the cargo containment system (CCS) for LNG carriers. In this paper, the features of a new independent type B CCS were firstly highlighted in comparison with the CCSs of conventional membrane-type and MOSS independent spherical type of the liquefied natural gas (LNG) carriers. In the following, a new thermal insulation system for the new independent type B CCS was designed and discussed. The conductivities of the insulation materials were tested and the heat transfer model for one typical tank of this carrier was established and simulated by using ANSYS Fluent software based on the analyses of the hull and CCS structures. The boil off rate (BOR) and temperature field for the new CCS were obtained based on the numerical simulation, in order to quantitatively evaluate the thermal insulation performance. It was found that the new independent type B CCS could efficiently prevent the environment heat inflow for the LNG vaporization and ensure the safety for the inner hull structures of the LNG carrier.

Let $A$ and $A'$ be two Artin groups of spherical type, and let $A_1,\dots,A_p$ (resp. $A'_1,\dots,A'_q$) be the irreducible components of $A$ (resp. $A'$). We show that $A$ and $A'$ are commensurable if and only if $p=q$ and, up to permutation of the indices, $A_i$ and $A'_i$ are commensurable for every $i$. We prove that, if two Artin groups of spherical type are commensurable, then they have the same rank. For a fixed $n$, we give a complete classification of the irreducible Artin groups of rank $n$ that are commensurable with the group of type $A_n$. Note that it will remain 6 pairs of groups to compare to get the complete classification of Artin groups of spherical type up to commensurability., Comment: 22 pages, 1 figure

The number of fabrication shop for spherical type LNG tank is proportional to that of the tank radius to be constructed. Due to limitation of facility investment including building sites, it is practically difficult to fabricate various size tanks with perfectly spherical shape in the yards. The efficient method to be capable of increasing cargo tank volume is to extend vertically the conventional spherical type LNG tank by inserting a cylindrical shell structure. The main purpose of this study is to derive related equations on forces generated on spherical type LNG tank with central cylindrical part under various static loadings in order to establish the simplified analysis method for the initial estimate. In this study, equations on circumferential and meridional force have been derived and verified by relations with the reaction forces per unit length of equator.

A conjecture of Dehornoy claims that, given a presentation of an Artin–Tits group, every word that represents the identity can be transformed into the trivial word using the braid relations, together with certain rules (between pairs of words that are not both positive) that can be derived directly from the braid relations, as well as free reduction, but without introducing trivial factors s s − 1 or s − 1 s . This conjecture is known to be true for Artin–Tits groups of spherical type or of FC type. We prove the conjecture for Artin–Tits groups of sufficiently large type.

We prove that the exponential growth rate of the regular language of penetration sequences is smaller than the growth rate of the regular language of normal form words, if the acceptor of the regular language of normal form words is strongly connected. Moreover, we show that the latter property is satisfied for all irreducible Artin monoids of spherical type, extending a result by Caruso. Our results establish that the expected value of the penetration distance $pd(x,y)$ in an irreducible Artin monoid of spherical type is bounded independently of the length of $x$, if $x$ is chosen uniformly among all elements of given canonical length and $y$ is chosen uniformly among all atoms; the latter in particular explains observations made by Thurston in the context of the braid group, and it shows that all irreducible Artin monoids of spherical type exhibit an analogous behaviour. Our results also give an affirmative answer to a question posed by Dehornoy., Comment: Published version

Spherical-type cations of 1-alkyl-4-aza-1-azoniabicyclo[2,2,2]octane (N-R DABCO, R = Me, Et) form ionic plastic crystals with BEt3Me− and BEt4−. Differential scanning calorimetry (DSC) analysis of ...

The distribution and abundance of oncoids in the shallow domains of a latest Kimmeridgian carbonate ramp was accomplished on the basis of a detailed sedimentological and petrographic analysis of the lower part of the Higueruelas Formation (Iberian Basin, northeastern Spain). Six types of oncoids are recognized based on the internal structure of the cortex, and show a preferential distribution on the carbonate ramp, which record from intertidal, lagoon, backshoal, shoal-sand blanket, foreshoal to offshore domains. Spherical type I oncoids, composed of continuous micritic laminae, occur in all the subenvironments in low proportions. Sub-spherical type II oncoids, constituted by micritic laminae and discontinuous organism-bearing laminae of mostly Bacinella irregularis, dominate in the higher-energy shoal-sand blanket domain. Type III oncoids, with alternating micritic and organism-bearing laminae of mostly Bacinella irregularis-Lithocodium aggregatum association, include two varieties: type IIIa oncoids, with micritic and organism-bearing laminae of similar thickness, preferentially formed in the foreshoal domain; and type IIIb oncoids, with thinner micritic laminae, formed in a low-energy sheltered lagoon. Irregular type IV oncoids characterize the low-energy settings, and include two varieties: type IVa oncoids, mainly consisting of a Bacinella-Lithocodium meshwork, which occur abundantly in the lagoon; and less abundant type IVb oncoids, composed of a continuous organism-bearing laminae of Lithocodium, which are found in the offshore domain. Water energy and platform morphology played an important role in formation and distribution of the oncoids in these shallow domains, where normal-marine water and oligotrophic conditions are highlighted by the high-diversity of light-dependant micro-encrusters in type III and IV oncoids. Comparable oncoid distribution patterns of diverse Late Jurassic shallow carbonate platforms enhance their potential use as reliable palaeoenvironmental proxies.

We give a complete classification of conjugacy stable parabolic subgroups of Artin-Tits groups of spherical type. This answers a question posed by Ivan Marin and generalizes a theorem obtained by Juan Gonz\'alez-Meneses in the specific case of Artin braid groups., Comment: Preliminary version; any comment welcome

International audience; The minimal standardizer of a curve system on a punctured disk is the minimal positive braid that transforms it into a system formed only by round curves. In this article, we give an algorithm to compute it in a geometrical way. Then, we generalize this problem algebraically to parabolic subgroups of Artin–Tits groups of spherical type and we show that, to compute the minimal standardizer of a parabolic subgroup, it suffices to compute the pn-normal form of a particular central element.

Spherical type(구형) LNG 운반선의 구형 탱크는 IMO 가스코 드(IGC)에서 독립형 탱크 Type B 방식으로 분류된다. 구형 탱크의 형상은 기하학적으로 가장 안전한 내압력 용기이며 선체와 탱크가 분리되어 있어 충돌이나 좌초 시 가장 안전한 구조 이다. Choe, et al. (2001)은 LNG 운반선의 충돌 강도 비교 연구를 통해 구형 LNG 운반선이 멤브레인형 LNG 운반선에 비해 더 많은 충돌에너지를 흡수할 수 있다고 발표한 바도 있다. 또한 화물창에 대한 슬로싱 문제가 없어 파이프 타워 해석에서만 부분적재(partial filling)에 대한 슬로싱 해석을 수행하면 된다 (Noh, 2005). 탱크 내 에는 보강재가 없어 균열(crack) 발생을 최소화 할 수 있는 등 많은 장점을 갖고 있으나, 가격이 비싸다는 단점을 가지고 있다. 가격이 비싸기 때문에 초기 견적 시 정도 높은 물량 계산이 필 수적이다. 하지만, 매번 유한요소해석을 통한 구조해석을 수행하 기에는 많은 시간과 노력이 소요되므로 정도 높은 간이해석법을 정립할 필요가 있다. 구형 탱크의 구조강도 관련 연구는 피로강도 (Nho, et al., 1993), 균열진전 (Nho, et al., 1993), 열 및 저온 (Kim, et al., 1993; Lee, et al., 1998; Nam, et al., 1993) 등의 연구가 비교적 활발히 수행되어 왔으나, 탱크의 초기 설계 및 물량 산출과 관련된 연구는 미진한 편이다. 구형 탱크의 초기 설계를 위한 연구 (Kim, 2000)가 수행된 바 있으나, 하중 조건이 모두 고려되지 못하였고, 유한요소해석으로 수행된 경계조건도 실제 조건과 많이 다르며, 해석 결과와 설계 제작 모델과의 두께 차가 크게 나타났다. 구의 형상은 이론적인 해를 구하기가 용이한 특징이 있어 실 제 구조해석 결과와 차이가 적을 것이라고 판단된다. 따라서, 본 연구에서는 이론적인 접근 방법을 기반으로 DNV와 LR 등의 선급 자료를 참고하여 간이해석법 정립을 시도하였다. 또한, 실 제 구조해석에서 적용하는 정적 하중 및 동적 하중을 모두 처리 할 수 있도록 구성한 것이 특징이며, 정립된 해석법의 결과를 실적선 구형 탱크의 두께 및 중량과 비교하여 그 유용성을 검증 하였다.

This paper presents the judgment method of the rehabilitation extent using a spherical type digital finger force measuring system (SDFFMS). Stroke patients can’t use their fingers because of the paralysis of their fingers, but they can recover with rehabilitative training. The SDFFMS has been already developed by Kim (Author of this paper), and the finger grasping forces of normal people and stroke patients could be measured using it. But the SDFFMS could be not used to judge the extent of their rehabilitation, because the judgment method using it is not yet developed. In this paper, the characteristics tests for the grasping forces of normal persons and stroke patients were performed using the SDFFMS, and the judgment method of the rehabilitation extent was developed using the results. The tests confirm that the rehabilitation extent of stroke patients could be judged using the developed judgment method.

The effect of compression storage on adsorption property of silicone rubber in silicone rubber-stainless steel interfacial system and silicone rubber-simulated X material interfacial system was studied in the paper by means of adsorption force testing and SEM statistical calculation method. The results of adsorption force testing indicated that surface roughness, sample type and compression ratio had important influence on adsorption, i.e. smooth surface tend to absorb, which implied that vacuum adsorption might be the main adsorption mechanism for silicone rubber interfacial systems. Plane-type, spherical type and inclinded plane type of samples had different degree of adsorption. Stainless steel interface tended to have larger adsorption than simulated X material interface. Higher compression ratio might lead to higher adsorption force. A SEM statistical calculation method was proposed to estimate the maximum vacuum adsorption force, and the maximum measurement result of adsorption force was approaching to the calculated maximum vacuum adsorption force by the proposed SEM method.

We study transnormal spherical partial tubes about transnormal submanifolds in Euclidean spaces. We put a necessary condition on the radius of the spherical type fibre so that such partial tubes are embeddings. We calculate radii of particular transnormal spherical partial tubes, which are embeddings of a torus in R 4 .

One of the most efficient designs for manufacturing LNG tank is the Moss spherical type because it has been validated through precise analyses with respect to reliability and construction safety by stress analysis. The Moss spherical tank is assembled with hundreds of Al thick plate patches that are deformed to curved shape at elevated temperature and welded together. It is essential to evaluate the amount of deflection in the Al5083 thick plate when the patch is transferred from the heating chamber to the forming die since the patch has a length of 12,000 mm and a thickness of 60 mm. Based on FE analysis results, a design procedure for minimizing deflection in Al5083 thick plate during transfer using a moving carrier is demonstrated in this paper.

Some patients cannot use their hands because their fingers are paralysed. Their fingers can recover with rehabilitative training and the extent of rehabilitation can be judged by grasping a spherical object with their fingers. This study looks at the development of a six-axis force/moment sensor and a spherical-type finger force measuring system with it which can measure grasping force. The six-axis force/moment sensor was designed and fabricated and a high-speed force measuring device was designed and manufactured by using digital signal processing. Also, the characteristic tests of the developed six-axis force/moment sensor and the spherical-type finger force measuring system were carried out. The tests confirm that the developed six-axis force/moment sensor is very good in interference error, and it can be used for the spherical-type finger force measuring system.

【In this study, gradient porous Al-Cu sintered body was fabricated by powder metallurgy processing. Al-Cu powder mixtures were prepared by low energy ball milling with various milling time. After ball milling for 3h, the shape of powder mixtures changed to spherical type with size of 100~500 ${\mu}m$ . Subsequently, Al-Cu powder mixtures were classified (under 150, 150~300 and over 300 ${\mu}m$ ) and compacted (20, 50 and 100 MPa). Then, they were sintered at $600^{\circ}C$ for various holding time (10, 30, 60 and 120 min) in $N_2$ atmosphere. The sintered bodies had 32~45% of porosity. As a result, the optimum holding time was determined to be 60 min at $600^{\circ}C$ and sintered bodies with various porosity were obtained by controlling the compacting pressure.】

In previous research, results on efficiency versus size and type of Ag particles showed similarity of detection efficiency comparing the particles of flake and spherical type with the gray particle on the market and in the case of nAg (rod, ) particle, relatively good results was given in the various evaluation methods for detection efficiency of latent fingerprint. However, oxidation was occurred when nAg particles laying on nature condition for a month and due to water absorption, detection efficiency was decreased. Therefore, with need to prevent oxidation and water absorption, more research is necessary. In this research, surface modification on nAg particles using silicon oil was conducted in various methods for complementing weakness of oxidation and water absorption. Then detection efficiency of nAg particles and surface modified nAg particles was evaluated by the number of feature points on the surface of non-porous materials (glass, plastic etc.) and degree of particle adhesion with ridges and contrast of detected fingerprint. Improvement of preventing oxidation and water absorbtion was given by surface modification using silicon oil (DC200, 0.5%) on the surface of non-porous materials.

We present all second order classical integrable systems of the cylindrical type in a three dimensional Euclidean space E3 with a nontrivial magnetic field. The Hamiltonian and integrals of motion have the form H =½ (p+A(x))2+W(x), X1=(p A)2+s1 r(r, , Z)pr A+s1 (r, , Z)p A+s1 Z(r, , Z)pZ A+m1(r, , Z), X2=(pZ A)2+s2 r(r, , Z)pr A+s2 (r, , Z)p A+s2 Z(r, , Z)pZ A+m2(r, , Z). Infinite families of such systems are found, in general depending on arbitrary functions or parameters. This leaves open the possibility of finding superintegrable systems among the integrable ones (i.e. systems with 1 or 2 additional independent integrals).

We consider algebraic and topological generalisations of braid groups and pure braid groups, namely Artin–Tits groups (of spherical type) and surface (pure) braid groups, and we determine their lower central series and related residual properties.

We compute the best constants of approximation by entire functions of spherical type and by trigonometric polynomials of spherical degree on classes of functions f satisfying the condition @[email protected]^[email protected]?"L"""p=

Effects of templating on the catalytic performance of SAPO-34 catalyst have been investigated in conversion of methanol to olefins (MTO). SAPO-34 catalysts were synthesized using a single agent or a mixture of morpholine or tetraethyl ammonium hydroxide of (TEAOH) as the template during synthesis of gel with nominal composition as 1Al2O3:1P2O5:0.6SiO2:x morpholine:(2 − x)TEAOH:52H2O. Compared with using single template, using a mixed template leads to the particle size reduction and the morphology change to spherical type formed by the aggregation of nano-sized crystals. Although all the catalysts showed similar activity and product distribution in the MTO reaction, the catalyst obtained using the mixture of 75% morpholine and 25% TEAOH gave the longest lifetime.

Gamma ray spectra analyses using unfolding techniques and dose evaluation are performed widely in the fields of environmental radiation monitoring and related environmental research. But generally the sizes and shapes of NaI(Tl) scintillation detectors of available response functions are limited: usually 3"φ×3" cylindrical or 3"φ spherical type, the energy range is roughly up to 3 MeV. In this paper, the response functions of eight types of cylindrical and spherical NaI(Tl) scintillation detectors (1"φ×1", 2"φ×2", 3"φ×3", 4"φ×4", 5"φ×4" cylindrical, and 2"φ, 3"φ, 5"φ spherical) were determined. The energy ranges were extended to 10 MeV maximum. Some response functions reported in the literature were unfolded using our response matrix for comparison, and the relative characteristics were discussed.

Let ( A , S ) be an Artin–Tits system, and A X be the standard parabolic subgroup of A generated by a subset X of S . Under the hypothesis that the Deligne complex has a CAT ( 0 ) geometric realization, we prove that the normalizer and the commensurator of A X in A are equal. Furthermore, if A X is of spherical type, these subgroups are the product of A X with the quasi-centralizer of A X in A . For two-dimensional Artin–Tits groups, the result still holds without any sphericality hypothesis on X . We explicitly describe the elements of this quasi-centralizer.

The present article generalizes the group-theoretical exchange condition to the theory of association schemes. We prove that a large class of association schemes satisfying our exchange condition arises from groups as quotients over subgroups. The result provides an alternate proof of Tits' reduction theorem for buildings of spherical type.

Let A S and A T be Artin–Tits groups and let ϕ p : A S → A T be an LCM -homomorphism constructed using the folding method. We characterize the quasicentralizer of ϕ p (S) in A T in the case when T is of spherical type.

The origins of carrier particles of complex particles (iron-rich particles) collected from the urban atmospheric environment near to road traffic and a railroad were investigated from the detailed surface information using FE-SEM/EDS and TOF-SIMS analyses. From the FE-SEM/EDS analyses, the iron-rich particles were classified into two typical types (spherical type and non-spherical type). From the TOF-SIMS measurements, the characteristic secondary ions of spherical type of iron-rich particles were 23 Na + and 39 K + . The minor components of non-spherical type were Al, Ca and Ba. On the other hand, we carried out TOF-SIMS measurement to materials of rail origin and brake origin. From the comparison of these spectra pattern, it seemed that the spherical type of iron-rich particles was emitted from the rail origin. We concluded that the origin of non-spherical type of iron-rich particles were brake pad of vehicles.

A semisolid microstructure of Mg 2 Si/Al composite is successfully achieved by isothermal heat treatment process, and the effects of holding temperature on semisolid microstructure of the composites are investigated. The result shows that, at the low heat treatment temperature, the morphology of primary Mg 2 Si particles are identified as irregular shape and α-Al grains exhibit elliptic and/or rosette type, and their sizes are non-uniform from 35 to 130 μm and 41 to 191 μm, respectively. With the increasing of treatment temperature, the morphologies of primary Mg 2 Si and α-Al grains change to spherical type, and their sizes decrease and become relatively uniform.

We show that symmetric spaces and thick affine buildings which are not of spherical type $A_1^r$ have no coarse median in the sense of Bowditch. As a consequence, they are not quasi-isometric to a CAT(0) cube complex, answering a question of Haglund. Another consequence is that any lattice in a simple higher rank group over a local field is not coarse median., 13 pages, 2 figures. To appear in Algebraic & Geometric Topology

Microleakage is a major factor contributing to the occurrence of secondary caries around amalgam restorations. Purpose The purpose of this study was to evaluate the effect of amalgam type, liner type, and storage period on microleakage.Two hundred seventy bovine incisors were divided into 18 groups (n = 15). Two high-copper amalgam alloys (admixed and spherical type) and 3 liner options (no liner, varnish, and adhesive) were used to restore Class V preparations. After placement of restorations, the teeth were stored for 3 different periods (1 day, 1 week, and 12 months) in saline solution, After storage, the specimens were immersed in 0.5% methylene blue for 24 hours, sectioned, and then mean depth of dye penetration was measured separately for the incisal and cervical areas with the use of a binocular microscope (x200). Scores were assigned to a millimeter scale (+/- 0.2 mm). The data were analyzed with a 3-way analysis of variance and the Tukey Honestly Significant Different test (alpha = .05).The 3-way interaction was significant (P.001 for the cervical and occlusal margins). After short-term storage (1 day and 1 week), the admixed alloy showed significantly lower leakage values than the spherical alloy only in cervical margins (1.45 and 1.56 for the admixed and 1.62 and 1.50 for the spherical alloy at the cervical [P = .034] and incisal margins [P = .702]), respectively. After 12 months, values decreased significantly for both amalgams, which were similar and lower than for the short-term storage period (short-term values of 1.62 and 1.39 for the admixed and 1.69 and 1.46 for the spherical alloy at the cervical and incisal margins, respectively; long-term values of 0.22 and 0.20 for the admixed and 0.33 and 0.36 for the spherical alloy at the cervical and incisal margins, respectively [P.019]). When the adhesive was used, significantly superior sealing was observed for both amalgams. For the no liner and cavity varnish groups, the admixed alloy showed superior performance compared to the spherical alloy (with no liner, 1.11 and 0.98 for the admixed and 0.83 and 1.08 for the spherical alloy at the cervical and incisal margins, respectively; with varnish, 1.19 and 1.22 for the admixed and 1.63 and 1.34 for the spherical alloy, at the cervical and incisal margins, respectively [P.037]).In the short-term, the lowest degree of leakage was found when adhesive was used. After 1 year, no differences were detected, regardless of the amalgam type and liner used.

A theoretical approach is developed for investigation of diffusion within nanometric or micrometric spherical-type domains limited by two types of active interfaces. Typical representative examples of either system consist in: (a) insoluble droplets (defined by spherical cupolas) of electroactive liquids or redox dendrimers adsorbed onto an electrode surface placed in an electrolyte or (b) biological vesicles during exocytotic release occurring in living cells. In situation (a), the active interface is an infinitely small ring defined along the triple-phase interface at the junction between the droplet surface, the electrode surface, and the electrolyte. In situation (b), the interface is a nanometric pore connecting the inside of the vesicle to the outer medium. Either situation imposes extremely difficult conditions for modeling the diffusional behavior of these two systems because of: (a) the conflicting symmetries between the spherical domains shapes vis-a-vis the pore or ring active interface which acts as a diffusional sink or a source and (b) the near-infinite and heterogeneous concentration gradients which develop at the active interface. Despite these intrinsic severe difficulties, introducing an original conformal mapping transform leads to a great simplification of the numerical solution of diffusional problems. This allows the development of fast and extremely precise simulations of the problem at hand. The efficiency of the simulations is tested in each case by imposing diffusion-controlled conditions so as to examine situations which enhance the intrinsic difficulties of the problems. In this first part, only diffusion within the inner domain defined by the vesicle or the droplet is considered in simulations since this is the domain in which the most difficult diffusional situations occur, but the general theory developed encompasses the most global circumstances, viz., when diffusion in both the inner and outer domains controls the system’s behavior and when generalized Butler–Volmer-type kinetics apply at the active interface. It is also shown that this conformal mapping approach leads to the design of a one-dimensional approximation which provides results accurate within a few percent compared to the full treatment of the system. Such equivalence, which is reminiscent of the hemisphere-disk or hemicylinder-band equivalence at ultramicroelectrodes, provides efficient and accurate simulations of the system at hand and may prove extremely valuable for semi-quantitative predictions.

Garside groups are a natural family generalizing Artin–Tits groups of spherical type. Most properties of the latter extend to arbitrary Garside groups. However some properties, in particular those involving conjugacy, require an additional technical criterion, called tameness, introduced by Charney et al. in [Geom. Dedicata 105 (1) (2004) 171–188]. In this paper, we establish an effective tameness criterion. This criterion turns out to apply to the Garside group that was the most natural candidate for nontameness.

Geostatistical conditional simulation is widely used and accepted as a method of generating stochastic models of hydrocarbon reservoirs. There are many applications described in the literature using one or more of the range of methods now available, and apart from the petroleum reservoirs, simulated annealing technique is applied to the total organic carbon values of the potential hydrocarbon source—rocks which has been penetrated by seven wells drilled on the western Taurus region. The main source rock intervals are mostly encountered in the autochthonous Beydaglari carbonates. After a description of the geology of the area a geostatistical study based on 440 composite samples is presented. The composite samples gave a positively skewed distribution with a mean of 0.27% total organic carbon values. Experimental variograms representing three main directions—strike plunge, cross dip, and downdip directions—were calculated a spherical type model was fitted to variograms. A model validation and a nu...