Surfaces S1 Research Articles

Anisotropic media with singular slowness surfaces

It is proved that if an anisotropic medium has an open set of singular directions, then this medium has two slowness surfaces that completely coincide. The coinciding slowness surfaces form one double singular slowness surface. The corresponding anisotropic medium is an elliptical orthorhombic (ORT) medium with equal stiffness coefficients c44=c55=c66 rotated to an arbitrary coordinate system. Based on the representation of the Christoffel matrix as a uniaxial tensor and considering that the elements of the Christoffel matrix are quadratic forms in the components of the slowness vector, a system of homogeneous polynomial equations was derived. Then, the identical equalities between homogeneous polynomials are replaced by the equalities between their coefficients. As a result, a new system of equations is obtained, the solution of which is the values of the reduced (density normalized) stiffness coefficients in a medium with a singular surface. Conditions for the positive definite of the obtained stiffness matrix are studied. For the defined medium, the Christoffel equations and equations of group velocity surfaces are derived. The orthogonal rotation matrix that transforms the medium with a singular surface into an elliptic ORT medium in the canonical coordinate system is determined. In the canonical coordinate system, the slowness surfaces S1 and S2 waves coincide and are given by a sphere with a radius . The slowness surface of qP waves in the canonical coordinate system is an ellipsoid with semi-axes , , . The polarization vectors of S1 and S2 waves can be arbitrarily selected in the plane orthogonal to the polarization vector of the qP wave. However, the qP wave polarization vector can be significantly different from the wave vector. This feature should be taken into account in the joint processing and modelling of S and qP waves. The results are illustrated in one example of an elliptical ORT medium.

Effects of composite coatings on pool boiling performance characteristics in demineralized water

Nucleate boiling is known for its high heat transfer capacity which occurs at a reasonably low temperature difference between the surface and saturated liquid due to the rapid vaporization process. The vaporization process and boiling heat transfer (BHT) primarily depend on surface morphology and wettability. In this article, surface morphology and wettability of smooth copper surfaces have been altered by coating with binary oxide nanoparticles. Three different combinations of composite coatings: TiO2/SiO2, TiO2/Al2O3 and SiO2/Al2O3 are considered and pool boiling performances have been investigated in demineralized water. Samples have been prepared using electrophoretic deposition techniques in binary oxide nanofluid of 0.1 wt. % concentration. The coating was performed for a fixed duration of 10 min in a medium of hybrid nanofluids of TiO2/SiO2, TiO2/Al2O3 and SiO2/Al2O3 which are referred to as S1, S2 and S3, respectively, in the text. The surface morphology, wettability and coating layer thickness of the sample are varied with the coating duration. The smooth copper surface is hydrophilic while coated samples are hydrophobic by nature. Experiments were carried out on all surfaces, and the results were compared with the smooth copper surface. The maximum enhancements in BHT coefficient for surfaces S1, S2 and S3 are 38%, 43% and 59%, respectively, corresponding to heat flux of ∼275,∼ 200 and ∼220 kW/m2. The reduction in boiling incipient temperature is 0.7, 3.6 and 4.4°C, respectively.

On Hopf hypersurfaces of [formula omitted] and [formula omitted

In this paper, we study Hopf hypersurfaces of the two Kähler surfaces S2×S2 and H2×H2. First, we classify real hypersurfaces of S2×S2 and H2×H2 with their shape operator A and induced almost contact structure ϕ satisfying Aϕ+ϕA=ρϕ for a constant ρ. Then, we classify real hypersurfaces of H2×H2 with isometric Reeb flow. Finally, we classify Hopf hypersurfaces of S2×S2 and H2×H2 with constant Reeb function as well as with recurrent Ricci tensor.

LiDAR‐based semi‐automated mapping of drumlins and mega‐scale glacial lineations of the Green Bay Lobe, Wisconsin, USA: Ice sheet beds as glaciotribological systems

AbstractA machine learning methodology for processing and visualizing high‐resolution LiDAR digital data is used to map drumlins and mega‐scale glacial lineations (MSGLs) on the bed of the Late Wisconsin Green Bay Lobe in Wisconsin, USA, which exhibited surge‐like behaviour during deglaciation. Previous work has shown that streamlined bedforms are the product of erosional streamlining of pre‐existing sediment. Analysis of bedform height and elongation ratio using curvature‐based relief separation (CBRS) andK‐means clustering of 32,003 bedforms reveals a continuum of six morphotypes ranging from drumlins, through “channeled” more elongated multi‐crested drumlins, to MSGLs. Further statistical analysis shows that morphotypes cluster into six types of streamlined surfaces (S1–S6) recording progressive elimination of an antecedent overridden topography to produce a smoother bed. Initial, relatively high‐relief drumlinized surfaces (S1, S2) occur around the slower‐flowing lateral flanks of the lobe, where a pre‐existing hummocky morainal topography was only partially modified by subglacial erosion. More streamlined surfaces (S3, S4) dominated by multi‐crested more elongate drumlins of reduced relief amplitude are transitional to flow sets of MSGL‐dominated surfaces (S5, S6) indicative of much faster‐flowing ice streaming along the lobe's axis. Estimates of basal drag based on roughness calculations for each surface type identify a 61% reduction in frictional retardation from poorly streamlined surfaces S1 and S2 to MSGL‐dominated surfaces S5 and S6, with a step‐like reduction between drumlins and channeled drumlins (S3, S4) possibly recording the rapid onset of fast flow. Subglacial streamlining is argued to be accomplished by a thin (<1 m) “third layer” of deforming subglacial debris between ice and its bed which functioned as an erodent layer. A thin (<3 m) till cap, formed by aggradation of deforming debris, rests unconformably on heterogeneous core sediments. Streamlined subglacial surfaces are comparable to the “functional” surfaces resulting from erosion by a “third layer” of wear debris in engineering tribological systems, and also by gouge on faults. Pleistocene ice sheets expanded over pre‐existing landsystems, pointing to the broader relevance of the methodology and findings reported here.

Numerical Analysis of Natural Convection Driven Flow of a Non-Newtonian Power-Law Fluid in a Trapezoidal Enclosure with a U-Shaped Constructal

Placement of fins in enclosures has promising utilization in advanced technological processes due to their role as heat reducing/generating elements such as in conventional furnaces, economizers, gas turbines, heat exchangers, superconductive heaters and so forth. The advancement in technologies in power engineering and microelectronics requires the development of effective cooling systems. This evolution involves the utilization of fins of significantly variable geometries enclosed in cavities to increase the heat elimination from heat-generating mechanisms. Since fins are considered to play an effective role in the escalation of heat transmission, the current study is conducted to examine the transfer of heat in cavities embedding fins, as well as the effect of a range of several parameters upon the transmission of energy. The following research is supplemented with the interpretation of the thermo-physical aspects of a power-law liquid enclosed in a trapezoidal cavity embedding a U-shaped fin. The Boussinesq approximation is utilized to generate the mathematical attributes of factors describing natural convection, which are then used in the momentum equation. Furthermore, the Fourier law is applied to formulate the streaming heat inside the fluid flow region. The formulated system describing the problem is non-dimensionalized using similarity transformations. The geometry of the problem comprises a trapezoidal cavity with a non-uniformly heated U-shaped fin introduced at the center of the base of the enclosure. The boundaries of the cavity are at no-slip conditions. Non-uniform heating is provided at the walls (l1 and l2), curves (c1,c2 and c3) and surfaces (s1 and s2) of the fin; the upper wall is insulated whereas the base and sidewalls of the enclosure are kept cold. The solution of the non-dimensionalized equations is procured by the Galerkin finite element procedure. To acquire information regarding the change in displacement w.r.t time and temperature, supplementary quadratic interpolating functions are also observed. An amalgam meshing is constructed to elaborate the triangular and quadrilateral elements of the trapezoidal domain. Observation of significant variation in the flow configurations for a specified range of parameters is taken into consideration i.e., 0.5≤n≤1.5 and 104≤Ra≤106. Furthermore, flow structures in the form of velocity profiles, streamlines, and temperature contours are interpreted for the parameters taken into account. It is deduced from the study that ascending magnitude of (Ra) elevates level of kinetic energy and magnitude of heat flux; however, a contrary configuration is encapsulated for the power-law index. Navier–Stokes equations constituting the phenomenon are written with the help of non-dimensionalized stream function, temperature profiles, and vortices, and the solutions are acquired using the finite element method. Furthermore, the attained outcomes are accessible through velocity and temperature profiles. It is worth highlighting the fact that the following analysis enumerates the pseudo-plastic, viscous and dilatant behavior of the fluid for different values of (n). This study highlights that the momentum profile and the heat transportation increase by increasing (Ra) and decline as the viscosity of the fluid increases. Overall, it can be seen from the current study that heat transportation increases with the insertion of a fin in the cavity. The current communication signifies the phenomenon of a power-law fluid flow filling a trapezoidal cavity enclosing a U-shaped fin. Previously, researchers have studied such phenomena mostly in Newtonian fluids, hence the present effort presents novelty regarding consideration of a power-law liquid in a trapezoidal enclosure by the placement of a U-shaped fin.

Neogene-Quaternary onshore record in the lower Ebro river incised palaeovalley (Ebro margin, Catalan Coastal Range, NE Iberia)

The lower Ebro is a bedrock-alluvial mixed incised valley with a persistent degradational stacking architecture developed from latest Serravallian(?) to Holocene. This degradational pattern was probably controlled by isostatic rebound in NE Iberia and punctuated by major relative sea level changes that temporally accentuated or attenuated the palaeovalley entrenchment and sediment retention. Six allostratigraphic units in the palaeovalley constitute the onshore record of its evolution and the opening and connection of the Ebro Basin with the Mediterranean. This paper deals with the analysis and reinterpretation of these units in order to precise the sequence of events that took place on the onshore part of the Catalan continental margin during the Ebro River drainage entrenchment. Plausible chronology and palaeogeographic evolution of the Neogene-Quaternary drainage incision in the lower Ebro are also proposed. The early evolutionary stages of the incised palaeovalley (Latest Serravallian?-Tortonian-Early Messinian, from 11.63–9? to near 5.6Ma) were dominated by entrenchment and intense sediment transfer from the onshore to the offshore zones (erosion surface S2). These processes were only punctuated by the sedimentation of the alluvial palaeovalley unit M2 (late Messinian). The polygenetic onshore erosion surfaces S2 and S3 are linked here with the onshore erosive processes that fed the sedimentation of the terrigenous shelf-slope system of the offshore Castellon group and considered coeval with the offshore Messinian erosion surfaces (reflectors M and m). During a further evolutionary stage (Pliocene to Early Pleistocene from 5.3 to approximately 2Ma) the Early Pliocene major Mediterranean reflooding caused some sediment retention in the incised palaeovalley (sedimentation of unit P) but sediment transfer into the offshore remained very effective. In the last evolutionary stage (Early Pleistocene-Holocene, from 2Ma to present) the palaeovalley became again mainly degradational (generation of erosion surfaces S4 to S6 and sedimentation of stepped alluvial terraces Q1-2 to Q4). The onshore stratigraphic record, including the allostratigraphic units P and Q1-2 to Q4 and the related bounding surfaces S3 to S6, is correlated with the sedimentation of the terrigenous shelf-slope system of the offshore Ebro group.

Lineament studies of rocks in Omifunfun area, southwestern Nigeria: Remote sensing and petrologic observations

Omifunfun area is situated in the southern part of Ife-Ilesa Schist Belt of the basement complex of southwestern Nigeria. The study area is traversed by the Ifewara Fault Zone which divides the area into east-west with contrasting lithologies that have been variously mylonitized. To the east, is quartzite and to the west migmatite gneiss which are intruded by prophyritic granites. The objective of this study is to delineate deformation linear structures from Landsat imageries over the study area, and attempt to correlate the information with microtectonic structures and field observations with the aim of better understanding the geologic terrain. Lineaments were extracted from Landsat images covering Omifunfun area. The analysis of these lineaments indicates low density in three prominentorientations corresponding to 0000–0350 and 0600–0900 with minor northwest-southeast structures. The most prominent of these directions is the 0000–0350 which incidentally include mylonite and mineral lineations within the Ifewara Fault system. Microtectonic observations reveal analogous results with three prominent foliation directions. The dominant one strikes in the same direction with the same Ifewara mylonitic foliation. These directions correspond to two major planar surfaces S1 and S2 and were respectively produced during two episodes of deformation (D1 andD2).KEYWORDS: Ifewara Fault Zone, Lineament, Microtectonic Structures, Mylonitization, Remote Sensing

Twistor Space for Rolling Bodies

On a natural circle bundle T(M) over a 4-dimensional manifold M equipped with a split signature metric g, whose fibers are real totally null selfdual 2-planes, we consider a tautological rank 2 distribution D obtained by lifting each totally null plane horizontally to its point in the fiber. Over the open set where g is not antiselfdual, the distribution D is (2,3,5) in T(M). We show that if M is a Cartesian product of two Riemann surfaces (S1,g1) and (S2,g2), and if g=g1--g2, then the circle bundle T(S1 x S2) is just the configuration space for the physical system of two solid bodies B1 and B2, bounded by the surfaces S1 and S2 and rolling on each other. The condition for the two bodies to roll on each other `without slipping or twisting' identifies the restricted velocity space for such a system with the tautological distribution D on T(S1 x S2). We call T(S1 x S2) the twistor space, and D the twistor distribution for the rolling bodies. Among others we address the following question: "For which pairs of bodies does the restricted velocity distribution (which we identify with the twistor distribution D) have the simple Lie group G2 as its group of symmetries?" Apart from the well known situation when the boundaries S1 and S2 of the two bodies have constant curvatures whose ratio is 1:9, we unexpectedly find three different types of surfaces, which when bounding a body that rolls `without slipping or twisting' on a plane, have D with the symmetry group G2. Although we have found the differential equations for the curvatures of S1 and S2 that gives D with G2 symmetry, we are unable to solve them in full generality so far.

The Messinian succession of the Crotone Basin (southern Italy) I: Stratigraphic architecture reconstructed by seismic and well data

The Messinian succession of the Crotone Basin, a forearc basin located along the Ionian side of the Calabrian Arc (southern Italy), is composed of resedimented gypsum, halite and siliciclastic subaqueous to continental deposits that are overlain by Lower Pliocene deep-marine marls. Integrated seismic and well data analysis have allowed the recognition of seven major stratal surfaces (S1–S7) of sequence stratigraphic significance and stratal units typified by diagnostic architectures, which allow to define three depositional sequences accumulated since the onset of the Messinian Salinity Crisis. This highlights an unusually complex stratigraphy that is interpreted as the result of the interplay between tectonics involving the basin and the Mediterranean-scale Messinian events. In particular, the surfaces S1 and S3, bounding the base and the top of the resedimented gypsum, and the uppermost surface (S7), bounding the base of the Pliocene succession, probably developed due to Mediterranean-scale events, specifically the onset and the end of the main base-level fall (S1 and S3, respectively) and the Early Zanclean reflooding (S7). The other surfaces are inferred to be related to basin-scale tectonics, although a relationship between local tectonics and pan-Mediterranean tectonic events linked to the Salinity Crisis cannot be ruled out. This, together with the evidence provided by other Messinian successions, raises the possibility that the base-level changes recorded in the Messinian deposits of the Mediterranean are more complex than previously thought, a possibility that deserves further investigations.

On the maximum number of cliques in a graph embedded in a surface

This paper studies the following question: given a surface Σ and an integer n, what is the maximum number of cliques in an n-vertex graph embeddable in Σ? We characterise the extremal graphs for this question, and prove that the answer is between 8(n−ω)+2ω and 8n+522ω+o(2ω), where ω is the maximum integer such that the complete graph Kω embeds in Σ. For the surfaces S0, S1, S2, N1, N2, N3 and N4 we establish an exact answer.

Study of the influence of the metal complex on the cytotoxic activity of titanocene-functionalized mesoporous materials

Four different titanocene complexes, [Ti(η5-C5H5)2Cl2] (1), [Ti(η5-C5H5)(η5-C5H4Pri)Cl2] (2), [Ti(η5-C5H5)(η5-C5H4But)Cl2] (3) and [Ti(η5-C5H5){η5-C5H3(SiMe3)2}Cl2] (4), have been grafted onto dehydroxylated MCM-41 to give the novel materials MCM-41/[Ti(η5-C5H5)2Cl2] (S1), MCM-41/[Ti(η5-C5H5)(η5-C5H4Pri)Cl2] (S2), MCM-41/[Ti(η5-C5H5)(η5-C5H4But)Cl2] (S3) and MCM-41/[Ti(η5-C5H5){η5-C5H3(SiMe3)2}Cl2] (S4), which have been characterized by powder X-ray diffraction, X-ray fluorescence, nitrogen gas sorption, multinuclear MAS NMR spectroscopy, thermogravimetry, UV spectroscopy, SEM and TEM. The cytotoxicity of the non-functionalized MCM-41 and S1–S4 toward human cancer cell lines, such as adenocarcinoma HeLa, human myelogenous leukemia K562 and human malignant melanoma Fem-x, has been studied. Additional studies of the toxicity of these materials on stimulated and non-stimulated peripheral blood mononuclear cells (PBMC + PHA and PBMC − PHA; i.e. normal immunocompetent cells) have been also carried out. M50 values (quantity of material needed to inhibit normal cell growth by 50%) of the studied surfaces are reported observing that non-functionalized MCM-41 did not show notable antiproliferative activity, while the functionalized surfaces S1–S4 were active against all of the studied human cancer cells. The cytotoxic activities of surfaces S1–S3 were very similar on all the studied cancer cells, however, S4 showed M50 values that indicate the highest activity of all the analyzed materials on all the studied cells, being two to three times more cytotoxic than S1–S3. The same tendency in the cytotoxic activity of the metal complexes 1–3 compared with 4 was observed. Taking into account that all the studied surfaces had a very similar titanium content, the activity of these surfaces strongly depends on the grafted titanocene complex (1–4). This phenomenon indicates that, in contrast with that observed by other authors, the cytotoxicity of the studied materials may be due to action of the released metal complex and is probably not due to the particle action.

Improvement of cytotoxicity of titanocene-functionalized mesoporous materials by the increase of the titanium content

The reaction of [Ti(eta(5)-C(5)H(5))(2)Cl(2)] (1), with 3-mercaptopropyltrimethoxysilane or 3-mercaptopropyltriethoxysilane in the presence of triethylamine leads to the formation of the thiolate complexes [Ti(eta(5)-C(5)H(5))(2){SCH(2)CH(2)CH(2)Si(OMe)(3)}(2)] (2) and [Ti(eta(5)-C(5)H(5))(2){SCH(2)CH(2)CH(2)Si(OEt)(3)}(2)] (3), respectively. Complexes 2 and 3 have been characterized by traditional methods, in addition, structural studies based on DFT calculations are reported. 1-3 have been grafted onto dehydroxylated MCM-41 to give the novel materials MCM-41/[Ti(eta(5)-C(5)H(5))(2)Cl(2)] (S1), MCM-41/[Ti(eta(5)-C(5)H(5))(2){SCH(2)CH(2)CH(2)Si(OMe)(3)}(2)] (S2) and MCM-41/[Ti(eta(5)-C(5)H(5))(2){SCH(2)CH(2)CH(2)Si(OEt)(3)}(2)] (S3) which have been characterized by powder X-ray diffraction, X-ray fluorescence, nitrogen gas sorption, multinuclear MAS NMR spectroscopy, thermogravimetry, UV spectroscopy, SEM and TEM. Materials S2 and S3 present much higher values of Ti wt% (ca. 3%) than S1 (ca. 1%), indicating the higher functionalization rate induced by the substitution of the chloro ligands by the thiolato ligands in the starting titanocene derivatives. The cytotoxicity of the non-functionalized MCM-41 and S1-S3 toward human cancer cell lines such as adenocarcinoma HeLa, human myelogenous leukemia K562 and human malignant melanoma Fem-x has been studied. In addition the cytotoxicity of these materials on normal immunocompetent cells such as stimulated (PBMC+PHA) and non-stimulated (PBMC-PHA) peripheral blood mononuclear cells have been also studied. M(50) values (quantity of material needed to inhibit normal cell survival by 50%) of the studied surfaces show that non-functionalized MCM-41 was not active against any of the studied cells, while the functionalized surfaces S1-S3 were active against all the tested human cancer cells. The cytotoxic activity of surfaces S2 and S3 were very similar, however, S1 showed lower cytotoxic activity. This phenomenon indicates that the cytotoxicity of the titanocene-functionalized materials strongly depends on the titanium content.

On foliations defined by harmonic functions

Riemann surfaces. A two-dimensional connected manifold S is called a Riemann surface if S is equipped with a complex atlas {Uα, zα} with biholomorphic functions zαz β (on their domains). The maximal atlas defines a conformal structure on S. Riemann surfaces S1 and S2 are said to be conformally equivalent if there is a conformal homeomorphism φ : S1 → S2 with conformal inverse. The complex plane C is a Riemann surface. Its conformal structure is determined by the atlas whose only chart is the identity mapping C → C. Every open connected domain D ⊆ C also becomes a Riemann surface in a natural way. The famous uniformization theorem claims that every noncompact simply connected Riemann surface is conformally equivalent to either C or the upper half-plane, which is conformally equivalent to the open unit diskD1 = {|z| < 1}. Let S be a Riemann surface with conformal structure {Uα, zα}. A function f : S → R is said to be harmonic on S if, for any chart Uα, the function f ◦ z−1 α is harmonic on zα(Uα). Kaplan [1] obtained the following remarkable result. Let F be a foliation without singularities on the plane R2. In this case, there are a conformal structure transforming R2 to a Riemann surface S and a harmonic function f on S such that the leaves of the foliation F are level curves of the function f . Following [1], we say that a foliation F is parabolic (hyperbolic, respectively) if S is conformally equivalent to C (to D1, respectively). Kaplan [1] proved that every foliation without singularities on the

TrackDip: A multi-scale processing of dipmeter data – Method, tests, and field example for 3-D description of gravity-driven deformations in the Eocene foreland basin of Ainsa, Spain

This paper presents TrackDip, a new method for dipmeter data processing. This method selects, localizes and measures significant tilts from the comparison at various scales of the changes of orientation of sedimentary beddings. We tested this method on simple cases (unconformity, gradual tilt, successive tilts, without and with additional random noise) and on a field example, along three sections in the Eocene Sobrarbe delta, Ainsa foreland basin, northern Spain. For synthetic data sets, the method clearly identifies and measures the introduced tilts. On the field, sedimentary and tectonic structures, especially three main syn-sedimentary sliding surfaces (S1–S3), were successfully identified from processed dipmeter data. The tilt axis are mainly trending N–S in sandstones, associated to Westward transport of sediments. The sliding surfaces S1 and S3 correspond to E–W-trending tilt axis, tentatively correlated either to the flexural subsidence of the basin, or to anticline growth during sedimentation South of the studied area. Combination of these sedimentary and tectonic directions results in a NE–SW striking submarine slope, which locally controls the gravity-driven deformations, especially on the S2 sliding surface. Finally, NNW–SSE-trending tilts above the uppermost S3 sliding surface are interpreted as the result of infilling on the side of the scar produced by sliding.

The unstable integral homology of the mapping class groups of a surface with boundary

We construct a graph complex calculating the integral homology of the bordered mapping class groups. We compute the homology of the bordered mapping class groups of the surfaces S 1,1, S 1,2 and S 2,1. Using the circle action on this graph complex, we build a double complex and a spectral sequence converging to the homology of the unbordered mapping class groups. We compute the homology of the punctured mapping class groups associated to the surfaces S 1,1 and S 2,1. Finally, we use Miller’s operad to get the first Kudo–Araki and Browder operations on our graph complex. We also consider an unstable version of the higher Kudo–Araki–Dyer–Lashoff operations.

Paleosurfaces from northeastern Amazonia as a key for reconstructing paleolandscapes and understanding weathering products

The characterization and mapping of paleoweathering surfaces, as well as their associated deposits, throughout the northeastern Amazonia can be a useful tool for inter-basin stratigraphic correlations and for establishing the evolution of landscapes and climates through time. This type of investigation has led to the recognition of five weathering surfaces developed from the Upper Cretaceous through the Quaternary, designated here as S1 to S5. Surface S1 occurs at the top of Late Cretaceous deposits, represented by the Ipixuna/Cujupe succession, as well as on older Precambrian and Paleozoic rocks. Surface S2 marks the top of an indurated, massive, semi-flint 1 1 The term semi-flint is applied here for a flint-like fire clay consisting of indurated kaolinite, which develops no plasticity when grounds up. unit. For cases in which surfaces S1 and S2 are amalgamated, a thick, lateritic paleosol displaying hexagonal, branched concretions is present. Surface S3 occurs at the top of the Pirabas and lower portion of the Barreiras Formations of Late Oligocene/Early Miocene age, and it is also associated with paleosol, but has no lateritization. When surface S3 is amalgamated with surfaces S1 and S2, bauxite is present in association with the underlying laterites. Surface S4 bounds the top of the middle to upper Barreiras Formation of Middle Miocene age, as well as correlatable deposits known as the Belterra Clay. This surface is marked by a lateritic paleosol having columnar concretions. Surface S5 occurs between a lower unit consisting of massive, light red sands of the Plio-Pleistocene Post-Barreiras 1 sediments and an upper unit of yellow, eolian sands of the Holocene Post-Barreiras 2 Sediments. The paleoweathering surfaces present in the northeastern Amazonia enable the reconstruction of several depositional episodes represented by thin (only few meters thick) sedimentary units from the Late Cretaceous to the Quaternary. The creation of new accommodation space on subsiding areas gave rise to sediment accumulation during transgressions. Intervening weathering surfaces formed during significant falls in relative sea-level, associated with tectonically stable episodes. The overprinting of weathering surfaces formed during different times, and thus under different climatic conditions, seems to have been crucial for the development of the various weathering products observed throughout the region, which include economically important laterites, bauxites, semi-flint beds and kaolin deposits. This paper shows that the genesis of these deposits was controlled by the complex interplay of tectonics, climate, sediment deposition and erosion, resulting in a complex evolution of paleolandscapes.

ON FLIPS IN POLYHEDRAL SURFACES

Let V be a finite point set in 3-space, and let [Formula: see text] be the set of triangulated polyhedral surfaces homeomorphic to a sphere and with vertex set V. Let abc and cbd be two adjacent triangles belonging to a surface [Formula: see text]; the flip of the edge bc would replace these two triangles by the triangles abd and adc. The flip operation is only considered when it does not produce a self-intersecting surface. In this paper we show that given two surfaces S1, [Formula: see text], it is possible that there is no sequence of flips transforming S1 into S2, even in the case that V consists of points in convex position.

Polyphase Folding in Nugrus-Sikeit Area South Eastern Desert, Egypt

lithological constitution of Nugrus-Sikeit area comprises a sequence of dismembered ophiolites, tectonic melange association and arc assemblage. These older rocks are intensively deformed and intruded by intracratonic association, which within the mapped area, is represented by gabbros and the associated hornblendite together with younger granites. Planar and linear mesoscopic structures exhibited by the rocks of Nugrus-Sikeit area indicate that these rocks are involved in superimposed folding events and at least three fold generations (F1, F2 & F3) can be recognized. The F1 folds resulted in isoclined folding of S0, and other primary structures around WNW-ESE axes. This phase represents the main folding that affected the area. Besides establishing the WNW-ESE pattern of rock units, it was also responsible for the transposition of S0 into penetrative surfaces S1 accompanying low to medium grade regional metamorphism. The F2 folds refolded the F1 folds into upright to overturned and even recumbent folds about NW-SE axes together with the crenulation of S1 surfaces producing crenulation cleavage S2? The F3 folds are of mild intensity compared to the F1 and F2 generations. It neither appeared to disturb the orientation of the earlier structures nor accompanied by strong transposition foliation. Associated folds are of the mesodimension and maintain a fairly constant NNE-SSW trend.

Algebraic threefolds with two extremal morphisms

In [3] Mori gives a description of all extremal rays (extremal morphisms) arising on a smooth projective threefold with a numerically non-effective canonical bundle. Generally speaking, every smooth projective threefold V with a numerically non-effective canonical class Kv admits an extremal morphism π: V— → Y. The assumption that V admits a non-trivial pair of extremal morph-ismsimposes strong conditions on V. This is the essence of the Theorem 1.5 of the present work. In particular, we obtain a description of the threefolds which admit two biregular structures of conic bundles over non-singular surfaces S1 = Y1 and S2 = Y2. By the results of §3 the surfaces Sl and S2 must be either ruled surfaces with isomorphic basic curves, or S1 ≈ S2 ≈ P2.

HREM Observations of Deformation Recovery on and Near Surfaces of Eu2O3

Profile imaging technigue has been achieved very much in the field of surface science since it was first proposed. This work will show the deformation recovery on and near the surfaces of Eu2O3 under electron irradiation. The experiment was carried out in a JEOL-200CX high-resolution electron microscope. The Eu2O3 phase has a complex cubic structure with a=1.087 nm. A projected unit cell has been marked in Fig. la. It has been indicated that only Eu3+ ions , which are located in f.c.c. sublattice, appeared in HR images under certain defocus and in the thin areas of specimen. The structural character of Eu2O3 shown by HR images may be analyzed based upon comparing with that of simple f.c.c. structure.It can be seen from Fig. la that the surfaces of Eu2O3 are clean and Eu3+ ions on the (111) surfaces S1 and S2 moved /12 towards to the right (it is actually surface stacking fault). In Fig.lb the stacking fault on S2 was removed under electron irradiation but remained on S1. The stacking fault energy of Eu2O3 is high in the bulk. From Fig.l it can be known that the stacking fault energy may become lower on the (111) surface due to less constrained factors there. This kind of surface stacking fault is related to surface partial dislocations, and both of them may act as the main forms of surface deformation under electron irradiation.