Limitations of the Special and General Relativities and Their Isotopic Generalizations

The scientific scene of this century has been dominated by the special and general relativities. In this paper we first recall that these relativities were not conceived for unlimited physical conditions, but solely for exterior problems (motion of point-like test bodies in the homogeneous and isotropic vacuum). We then show that the relativities are inapplicable (rather than violated) for the more general interior problems (motion of extended test bodies within inhomogeneous and anisotropic physical media) on numerous, independent, topological, geometric, analytic and other grounds. We also outline the rather numerous problematic aspects of general relativity for exterior problems in vacuum, while the problematic aspects of the special relativity in vac- uum are treated elsewhere in this volume. We also point our rather serious insufficiencies of the special and general relativities for an effective representation of antimatter, beginning at a classicalwastrophysical level and then continuing at the operator-particle level. The paper ends with a brief outline of the so-called isotopic generalization of the special and general relativities initiated by this author back in 1978 when at Harvard University under support from the U. S. Department of Energy, and subsequently studied by a number of mathematicians, theoreticians and experimentalists. These isotopic studies are presented as an indication of the true scientific renaissance in mathematics, physics, superconductivity and other fields which has been stimulated by the limitations and problematic aspects of the special and general relativities. These studies are coordinated by the Istituto per la Ricerca di Base in Italy. All scholars interested in truly fundamental advances in mathematics, physics, superconductivity and other disciplines are encouraged to participate in this collegial ef- fort.

DIAGNOSIS AND TREATMENT OF INSIDIOUS RECURRENT SMALL INTESTINAL HEMORRHAGE

Objective. To improve the localized diagnosis of insidious recurrent small intestinal hemorrhage. Methods. This retrospective analysis include 64 cases of such diseases,which were admitted from 1988 to 1998 to our hospital. Result. Ultrasonography, CT, small bowel pneumobariumgraphy, diluted barium enema,isotopic examination, DSA and intraoperative small-bowel endoscopy were used for diagnosis of hemorrhagic site, and 37 cases got a definite location before operation,while 10 cases were confirmed the diagnosis during the operation.Forty-seven cases were treated surgically, while the other 17 cases had non-surgical treatment.Of the 47 cases,39 cases underwent partial enterectomy, 5 cases had suture and ligature of vascular deformity, 2 cases had Whipple’s operation, and one patient had ectomy of the end of ileum and right colon. Conclusion. DSA, Isotopic examination and intraoperative enteroscopy are of considerable importance for the location judgement of recurrent small intestinal hemorrhage.

Some Open Problems in Geometric Topologyof Low Dimensions

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Physico-Chemical and Isotopic (18O, 2H and 3H) Characterization of the Upper Dallol Maouri Watershed (Niger)

Dallol Maouri is one of the fossil valleys on the left bank of the Niger River. Its watershed drains water from valleys in the Tahoua and Dosso regions of Niger. The watercourse is not continuous and has areas of surface water accumulation (ponds) and areas of spreading and infiltration. The surface water potential in this area is limited, with most of the ponds having a temporary to the semi-permanent regime. Groundwater resources are, therefore, the main sources of withdrawal for human food, agriculture, and livestock. Climate change through the variation in rainfall, the often-anarchic multiplication of catchment works (wells and boreholes) and agricultural activities can have impacts on the qualitative and quantitative evolution of surface and groundwater. The objective of this study is to characterize the surface and underground water of the upper dallol Maouri through the physicochemical parameters of the water and the use of the isotopes of the water molecule (18O, 2H and 3H). A total of 53 water samples were analyzed at the laboratory of the Regional Directorate of Hydraulics and Sanitation of Tillabéri (Niger) for chemical parameters and 73 samples were analyzed at the Radio Analysis and Environment Laboratory (LRAE) of the National School of Engineers of Sfax (ENIS) of Tunis for isotopy. The water of the ponds is characterized by three types of facies: calcium bicarbonate, calcium and magnesium bicarbonate, and calcium nitrate chloride. The groundwater is 75% of the chloride-nitrate-calcium facies and the CT3/CT2 groundwater is calcium and magnesium bicarbonate. The results of the stable isotopes made it possible to highlight the presence of four distinct water groups: ponds characterized by highly evaporated water, the sheets of Continental Terminal 1 and 2 (CT1 and CT2) with an isotopic cachet of old water, the water table consisting of a two-layer system in the southwestern part of the area. The water is not very mineralized (40 μS to 600 μS) and is slightly acidic (pH = 6.4). The analysis of the radioactive isotope (3H) content of the water from the water table has made it possible to identify the areas of recharge of the water table. These results also highlight: the presence of an upward drainage zone, and the contribution of lowland ponds to the recharge of alluvial aquifers ranging from 24% to 84%. No structure in this zone reaches the Continental Intercalaire and the Continental Hamadien, the depth of which is estimated at an average of 600 m. The relationship between the 18O and 3H contents of groundwater water shows two types of water with tritium contents higher than 2 TU for alluvial aquifers and tritium contents lower than 2 TU for groundwater (CT3). The analysis of the radioactive isotope (3H) contents of the groundwater has made it possible to identify recent recharges at the level of the alluvial aquifers and in the outcrop zone of CT3. There is no hydraulic continuity between the plateau ponds and groundwater.

Climate Change Impact on Aquifer System of Essaouira Basin during the Past 4 Decades (Morocco)

Since the 50s, many changes are observed in the climate of the globe, the warming of the atmosphere and the ocean, the decrease in the extent of snow and ice, and rising sea levels. In addition to the demographic pressure, the Maghreb countries are suffering from the drought, which accentuates the phenomenon of desertification and soil erosion, as well as their salinity, which leads to the salinization and depletion of water resources. In Morocco, the climate change leads to the erosion of the soil under the effect of desertification resulting in siltation of reservoirs and the increased salinization of soil and water resources. The Essaouira basin, which is the subject of this study, is located at the Western extremity of the High Atlas to the Southeast of the Essaouira city;between 31°20' to 31°30'N and between 9°00' to 9°46'W. The basin is characterized by a semi-arid climate with average annual rainfall of around 300 mm·year-1 and an average temperature of 20°C. Considering the importance of the aquifer in Essaouira in the supply of the region's groundwater, a study was conducted to assess quantitatively and qualitatively the impact of climate change on water resources in this area. The aquifers present in this region are one of cenomano-turonian upstream and plio-quaternary downstream, separated by the diaper of Tidzi. A piezometric map of the basin was made (1990-2009) and the hydrochemical method of the waters shows that they present a facies Na-Cl with an electrical conductivity ranging from 700 to 7000 μs/cm. The isotopic tracers like 18O, 2H, 3H and 14C were analyzed to determine the age of groundwater, and a right local meteoric close to the right meteoric world characterizing the precipitation of oceanic origin has been determined. The Essaouira basin turns out to be very vulnerable and sensitive to climate change because its recharge is entirely dependent on the rainwater. These results should be taken in consideration for the future water management in the region.

The topology of moment-angle manifolds——on a conjecture of S. Gitler and S. López de Medrano

In this paper,we study the topology of moment-angle manifolds and prove a conjecture of S.Gitler and S.Lopez de Medrano concerned with the behavior of the moment-angle manifold under the surgery’cutting off a vertex’on a simple polytope.Let P be a simple polytope of dimension n with m facets and Pv be a poly tope obtained from P by cutting off one vertex v.Let Z=Z(P)and Zv=Z(Pv)be the corresponding moment-angle manifolds.S.Gitler and S.Lopez de Medrano conjectured that:Zv is diffeomorphic to δ[(Z(-D^n+m)×D^2]##^m-n/j=1(m-n/j)(S^j+2×S^m+n-j-1),and they proved the conjecture in the case m<3 n.In this paper we prove the conjecture in the general case.

A SIMPLIFIED APPROACH TO EMBEDDING PROBLEMS IN NORMAL BORDISM FRAMEWORK

The purpose of this paper is to simplify the computations of the nor-mal bordism groups Ωi（Wf,M×P∞;（?））and Ωi（Cf,（?）w;θf）which Salomonsenand Dax introduced respectively to study the existence and isotopy classificationof differential embeddings of manifolds in manifolds in the metastable range.Asimpler space pair（Kf,M×P∞）is constructed to replace（Wf,M×P∞）.It isshown that（Kf,M×P∞）is homotopy equivalent to（Wf,M×P∞）and homotopy（n-1）-equivalent to（Cf,（?）W）.To demonstrate the efficacy of this simplification,the isotopy groups [Mn（?）RPn+k],if n（?）2k-4 and Mn is a closed（n-k+2）-connected manifold,and[Mn（?）L（p;q1…,qm）],if 3n（?）4m-2,Mn is a closed（2n-2m+1）-connected manifold and L is a （2m+1）-dimensional lens space,arespecifically computed.

ENUMERATION OF LATIN ARRAYS (Ⅰ)——CASE n≤3

This paper introduces the concept of Latin arrays, discusses the general property on their enumeration, and gives formulae of numbers for (2,k)- and (3,k)-Latin arrays and for their isotopy classes.

Characteristic Class of Isotopy for Surfaces

It is an important problem in topology to verify whether two embeddings are isotopic.This work proposes an algorithm for computing Haefliger-Wu invariants for isotopy based on algebraic topological methods.Given a simplicial complex embedded in the Euclidean space,the deleted product of it is the direct product with diagonal removed.The Gauss map transforms the deleted product to the unit sphere.The pull-back of the generator of the cohomology group of the sphere defines characteristic class of the isotopy of the embedding.By using Mayer Vietoris sequence and Ku¨nneth theorem,the computational algorithm can be greatly simplified.The authors prove the ranks of homology groups of the deleted product of a closed surface and give explicit construction of the generators of the homology groups of the deleted product.Numerical experimental results show the efficiency and efficacy of the proposed method.

ENUMERATION OF LATIN ARRAYS(Ⅱ)——CASE n=4,k≤4

This paper gives numbers for (4,k, 1)-Latin arrays (1≤k≤3) and (4,k)-Latin array for(1≤k≤4) and for their isotopy classes.

Diffeomorphic types of complements of nice point arrangements in CP^l

We use a new method to study arrangement in CPl,define a class of nice point arrangements and show that if two nice point arrangements have the same combinatorics,then their complements are diffeomorphic to each other.In particular,the moduli space of nice point arrangements with same combinatorics in CPl is connected.It generalizes the result on point arrangements in CP3 to point arrangements in CPl for any l.

Some Characterizations of a Normal Subgroup of a Group and Isotopic Classes of Transversals

Let G be a group and H be a subgroup of G which is either finite or of finite index in G. In this paper, we give some characterizations for the normality of H in G. As a consequence we get a very short and elementary proof of the main theorem of a paper of Lal and Shukla, which avoids the use of the classification of finite simple groups. Further, we study the isotopy between the transversals in some groups and determine the number of isotopy classes of transversals of a subgroup of order 2 in D2p, the dihedral group of order 2p, where p is an odd prime and the isotopism classes are formed with respect to induced right loop structures.

GLI ISOTOPI DELL'OSSIGENO COME INFORMATORI PALEOCLIMATICI—— Alcuni dati sperimentali

Studi precedenti hanno permesso di definite l’esistenza di una retazione diretta e quantita-tiva che lega la composizione isotopica dell’ossigeno (18O/16O) nel fosfato delle ossa di diverse speciedi mammiferi con la temperatura media annua al suolo delle località di provenienza di tali animali.Potendo applicare tale relazione a campioni di mammiferi vissuti in età preistorica risulta evidente lapossibilità di compiere studi di tipo paleoclimatico e paleoidrologico. Si presentano i risuhati ottenuti da campioni provenienti da alcuni siti preistorici della Pianura Pada-na e dal villaggio di Fossacesia Marina sulla costa Adriatica. I dati isotopici si accordano bene con le informazioni sulla situazione climatica durante l’Atlanticoottenute con altre metodologie di studio; eventuali variazioni e fluttuazioni locali vengono discusse.Oxygen isotopes as climatic indicators. Some experimental data. Oxygen isotope composi-tion (18O/16O) of bone phosphate from different mammal species coming from some prehistoric sitesof the Po Valley and from the Neolithic village of Fossacesia Marina （CH） have been carried on. Previousstudies have demonstrated the existence of a direct, quantitative relationship between oxygen isotopiccomposition of bone phosphate and mean annual temperature. The existence of such relationship allowsto study the ancient environment and climate. The trend of climate, during prehistoric periods, agrees well with the data obtained from other me-thodology of study; some fluctuations of climate in the studied sites are also discussed.