Comparative statement of different classes of trade passing downward through the Welland Canal at Port Colborne during the years 1857-1861

Comparative statement of different classes of trade passing downward through the Welland Canal at Port Colborne during the years 1857-1861 (1 page, hand drawn chart), Jan.25, 1862.

Statement of classes of vessels and merchandise passing downward through the Welland Canal during the year 1857

Statement of classes of vessels and merchandise passing downward through the Welland Canal during the year 1857 (Port Colborne), Jan. 30, 1862.

English grammar, adapted to the different classes of learners with an appendix, containing rules and observations, for assisting the more advanced students to write perspicuity and accuracy

UANL

Clique Irreducibility of Some Iterative Classes of Graphs

In this paper, two notions, the clique irreducibility and clique vertex irreducibility are discussed. A graph G is clique irreducible if every clique in G of size at least two, has an edge which does not lie in any other clique of G and it is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G. It is proved that L(G) is clique irreducible if and only if every triangle in G has a vertex of degree two. The conditions for the iterations of line graph, the Gallai graphs, the anti-Gallai graphs and its iterations to be clique irreducible and clique vertex irreducible are also obtained.

Some classes of Turker equivalent graphs

Two graphs G and H are Turker equivalent if they have the same set of Turker angles. In this paper some Turker equivalent family of graphs are obtained.

The (t) property of some classes of graphs

In this note,the (t) properties of five class are studied. We proved that the classes of cographs and clique perfect graphs without isolated vertices satisfy the (2) property and the (3) property, but do not satisfy the (t) property for tis greater than equal to 4. The (t) properties of the planar graphs and the perfect graphss are also studied . we obtain a necessary and suffieient conditions for the trestled graph of index K to satisfy the (2) property

Development of a Technique for Estimating Rain Parameters from Rain Noise Measurements

The measurement of global precipitation is of great importance in climate modeling since the release of latent heat associated with tropical convection is one of the pricipal driving mechanisms of atmospheric circulation.Knowledge of the larger-scale precipitation field also has important potential applications in the generation of initial conditions for numerical weather prediction models Knowledge of the relationship between rainfall intensity and kinetic energy, and its variations in time and space is important for erosion prediction. Vegetation on earth also greatly depends on the total amount of rainfall as well as the drop size distribution (DSD) in rainfall.While methods using visible,infrared, and microwave radiometer data have been shown to yield useful estimates of precipitation, validation of these products for the open ocean has been hampered by the limited amount of surface rainfall measurements available for accurate assessement, especially for the tropical oceans.Surface rain fall measurements(often called the ground truth)are carried out by rain gauges working on various principles like weighing type,tipping bucket,capacitive type and so on.The acoustic technique is yet another promising method of rain parameter measurement that has many advantages. The basic principle of acoustic method is that the droplets falling in water produce underwater sound with distinct features, using which the rainfall parameters can be computed. The acoustic technique can also be used for developing a low cost and accurate device for automatic measurement of rainfall rate and kinetic energy of rain.especially suitable for telemetry applications. This technique can also be utilized to develop a low cost Disdrometer that finds application in rainfall analysis as well as in calibration of nozzles and sprinklers. This thesis is divided into the following 7 chapters, which describes the methodology adopted, the results obtained and the conclusions arrived at.

Betweenness Centrality in Some Classes of Graphs

There are several centrality measures that have been introduced and studied for real world networks. They account for the different vertex characteristics that permit them to be ranked in order of importance in the network. Betweenness centrality is a measure of the influence of a vertex over the flow of information between every pair of vertices under the assumption that information primarily flows over the shortest path between them. In this paper we present betweenness centrality of some important classes of graphs.

Fair Sets of Some Classes of Graphs

Given a non empty set S of vertices of a graph, the partiality of a vertex with respect to S is the di erence between maximum and minimum of the distances of the vertex to the vertices of S. The vertices with minimum partiality constitute the fair center of the set. Any vertex set which is the fair center of some set of vertices is called a fair set. In this paper we prove that the induced subgraph of any fair set is connected in the case of trees and characterise block graphs as the class of chordal graphs for which the induced subgraph of all fair sets are connected. The fair sets of Kn, Km;n, Kn e, wheel graphs, odd cycles and symmetric even graphs are identi ed. The fair sets of the Cartesian product graphs are also discussed

A STUDY OF THE TECHNIQUE OF THE HINDI DRAMA POST PRASAD PERIOD (1935 - 1965)

Hindi

Some New Classes of Orthogonal Polynomials and Special Functions

In dieser Dissertation präsentieren wir zunächst eine Verallgemeinerung der üblichen Sturm-Liouville-Probleme mit symmetrischen Lösungen und erklären eine umfassendere Klasse. Dann führen wir einige neue Klassen orthogonaler Polynome und spezieller Funktionen ein, welche sich aus dieser symmetrischen Verallgemeinerung ableiten lassen. Als eine spezielle Konsequenz dieser Verallgemeinerung führen wir ein Polynomsystem mit vier freien Parametern ein und zeigen, dass in diesem System fast alle klassischen symmetrischen orthogonalen Polynome wie die Legendrepolynome, die Chebyshevpolynome erster und zweiter Art, die Gegenbauerpolynome, die verallgemeinerten Gegenbauerpolynome, die Hermitepolynome, die verallgemeinerten Hermitepolynome und zwei weitere neue endliche Systeme orthogonaler Polynome enthalten sind. All diese Polynome können direkt durch das neu eingeführte System ausgedrückt werden. Ferner bestimmen wir alle Standardeigenschaften des neuen Systems, insbesondere eine explizite Darstellung, eine Differentialgleichung zweiter Ordnung, eine generische Orthogonalitätsbeziehung sowie eine generische Dreitermrekursion. Außerdem benutzen wir diese Erweiterung, um die assoziierten Legendrefunktionen, welche viele Anwendungen in Physik und Ingenieurwissenschaften haben, zu verallgemeinern, und wir zeigen, dass diese Verallgemeinerung Orthogonalitätseigenschaft und -intervall erhält. In einem weiteren Kapitel der Dissertation studieren wir detailliert die Standardeigenschaften endlicher orthogonaler Polynomsysteme, welche sich aus der üblichen Sturm-Liouville-Theorie ergeben und wir zeigen, dass sie orthogonal bezüglich der Fisherschen F-Verteilung, der inversen Gammaverteilung und der verallgemeinerten t-Verteilung sind. Im nächsten Abschnitt der Dissertation betrachten wir eine vierparametrige Verallgemeinerung der Studentschen t-Verteilung. Wir zeigen, dass diese Verteilung gegen die Normalverteilung konvergiert, wenn die Anzahl der Stichprobe gegen Unendlich strebt. Eine ähnliche Verallgemeinerung der Fisherschen F-Verteilung konvergiert gegen die chi-Quadrat-Verteilung. Ferner führen wir im letzten Abschnitt der Dissertation einige neue Folgen spezieller Funktionen ein, welche Anwendungen bei der Lösung in Kugelkoordinaten der klassischen Potentialgleichung, der Wärmeleitungsgleichung und der Wellengleichung haben. Schließlich erklären wir zwei neue Klassen rationaler orthogonaler hypergeometrischer Funktionen, und wir zeigen unter Benutzung der Fouriertransformation und der Parsevalschen Gleichung, dass es sich um endliche Orthogonalsysteme mit Gewichtsfunktionen vom Gammatyp handelt.

Constraints from the old quasar APM 08279+5255 on two classes of Lambda(t)-cosmologies

The viability of two different classes of Lambda(t)CDM cosmologies is tested by using the APM 08279+5255, an old quasar at redshift z = 3.91. In the first class of models, the cosmological term scales as Lambda(t) similar to R(-n). The particular case n = 0 describes the standard Lambda CDM model whereas n = 2 stands for the Chen and Wu model. For an estimated age of 2 Gyr, it is found that the power index has a lower limit n > 0.21, whereas for 3 Gyr the limit is n > 0.6. Since n can not be so large as similar to 0.81, the Lambda CDM and Chen and Wu models are also ruled out by this analysis. The second class of models is the one recently proposed by Wang and Meng which describes several Lambda(t)CDM cosmologies discussed in the literature. By assuming that the true age is 2 Gyr it is found that the epsilon parameter satisfies the lower bound epsilon > 0.11 while for 3 Gyr, a lower limit of epsilon > 0.52 is obtained. Such limits are slightly modified when the baryonic component is included.

On isomorphism classes of C(2(m) circle plus [0, alpha]) spaces

We provide a complete isomorphic classification of the Banach spaces of continuous functions on the compact spaces 2(m) circle plus [0, alpha], the topological sums of Cantor cubes 2(m), with m smaller than the first sequential cardinal, and intervals of ordinal numbers [0, alpha]. In particular, we prove that it is relatively consistent with ZFC that the only isomorphism classes of C(2(m) circle plus [0, alpha]) spaces with m >= N(0) and alpha >= omega(1) are the trivial ones. This result leads to some elementary questions on large cardinals.

The classification and the conjugacy classes of the finite subgroups of the sphere braid groups

Let n >= 3. We classify the finite groups which are realised as subgroups of the sphere braid group B(n)(S(2)). Such groups must be of cohomological period 2 or 4. Depending on the value of n, we show that the following are the maximal finite subgroups of B(n)(S(2)): Z(2(n-1)); the dicyclic groups of order 4n and 4(n - 2); the binary tetrahedral group T*; the binary octahedral group O*; and the binary icosahedral group I(*). We give geometric as well as some explicit algebraic constructions of these groups in B(n)(S(2)) and determine the number of conjugacy classes of such finite subgroups. We also reprove Murasugi`s classification of the torsion elements of B(n)(S(2)) and explain how the finite subgroups of B(n)(S(2)) are related to this classification, as well as to the lower central and derived series of B(n)(S(2)).