Ananda Marga counts hundreds of missions around the world through which its members carry out various forms of selfless service on Relief ( The social welfare and development organization under AMPS is Ananda Marga Universal Relief Team, or AMURT., Education and women's welfare ( The service activities of this section founded in 1963 are focused on: 1-Education: creating and managing primary, post primary and higher schools, research institutes etc., 2-Relief: creating and managing children's and students ' homes for destitute children and for poor students, cheap hostels, retiring homes, academies of light for deaf dumb and crippled, invalid homes, refuge reabilitation etc., 3-Tribal: tribal welfare units, medical camps etc., 4-Women's welfare: women welfare units, women's homes, nursing homes etc.

She taught physical training at various schools in England and Scotland, but in 1926 she had to return to Inverness to care for her invalid father.

There are various ways to combine such sentences into syllogisms, both valid and invalid.

No doubt largely because of his influence, various authors supported the term, either as such, or as " Urochordata ", but the usage is invalid because " Tunicata " has precedence and there never were grounds for superseding the name.

In June, 1089, at a Synod held in Rome, Clement III declared invalid the decree of excommunication launched against Henry, and various charges were made against the supporters of Urban II, the pope of the anti-imperial party.

Members of the public can also initiate lawsuits in the courts of various nations to have patents declared invalid.

This is because each time thousands of signatures presented are deemed invalid by the constitutional court on various grounds.

Volume 12, No. 323, July 19, 1828, " the modes of application are various: sometimes the invalid takes three draughts of it before anything is spoken.

Their lyrical content deals primarily with Satanism on a metaphysical level – as the band has stated that " all other interpretations of Satan are intellectually invalid " – and other various theological topics.

However, it is essential that the various mathematical symbols used in the equations be understood so that the mathematical processes can be done properly and in their correct order.

The various mathematical processes can be simplified by carrying the results to only two or three decimal places.

; Analysis of variance ( ANOVA ): A mathematical process for separating the variability of a group of observations into assignable causes and setting up various significance tests.

The absolute value is closely related to the notions of magnitude, distance, and norm in various mathematical and physical contexts.

He held that the Absolute Infinite had various mathematical properties, including the reflection principle which says that every property of the Absolute Infinite is also held by some smaller object.

Constructed languages such as Esperanto, programming languages, and various mathematical formalisms are not necessarily restricted to the properties shared by human languages.

The study of condensed matter physics involves measuring various material properties via experimental probes along with using techniques of theoretical physics to develop mathematical models that help in understanding physical behavior.

The study of categories is an attempt to axiomatically capture what is commonly found in various classes of related mathematical structures by relating them to the structure-preserving functions between them.

By studying categories and functors, we are not just studying a class of mathematical structures and the morphisms between them ; we are studying the relationships between various classes of mathematical structures.

Chemical thermodynamics involves not only laboratory measurements of various thermodynamic properties, but also the application of mathematical methods to the study of chemical questions and the spontaneity of processes.

It seeks to understand physical systems, using mathematical modeling, in terms of inputs, outputs and various components with different behaviors ; use control systems design tools to develop controllers for those systems ; and implement controllers in physical systems employing available technology.

In short, virtual manipulatives are dynamic visual / pictorial replicas of physical mathematical manipulatives, which have long been used to demonstrate and teach various mathematical concepts.

The principles underlying intra-and inter-individual differences could be educationally useful, because knowing how students differ in regard to the various dimensions of cognitive development, such as processing and representational capacity, self-understanding and self-regulation, and the various domains of understanding, such as mathematical, scientific, or verbal abilities, would enable the teacher to cater for the needs of the different students so that no one is left behind.

Indeed, according to various historical accounts, after that point few mathematicians tackled the issues and the work of those who did remained obscured largely because of resistance to such unfamiliar emerging concepts, which were sometimes referred to as mathematical " monsters ".

Hedge fund managers can use various types of analysis to identify price discrepancies in securities, including mathematical, technical or fundamental techniques.

Kepler calculated and recalculated various approximations of Mars ' orbit using an equant ( the mathematical tool that Copernicus had eliminated with his system ), eventually creating a model that generally agreed with Tycho's observations to within two arcminutes ( the average measurement error ).

He discovered ways to express various logarithmic functions using power series, and he successfully defined logarithms for negative and complex numbers, thus greatly expanding the scope of mathematical applications of logarithms.

The ambition of geometric model theory is to provide a geography of mathematics by embarking on a detailed study of definable sets in various mathematical structures, aided by the substantial tools developed in the study of pure model theory.

The set has a number of important mathematical properties that are foundational to various branches of mathematics.

Further work continues to find mathematical constructs that join various surrounding theories.

Prime numbers give rise to various generalizations in other mathematical domains, mainly algebra, such as prime elements and prime ideals.

Since then, many alternate proofs have been found out by various authors as collected in ().

These principles are widely used intuitively in various kinds of proofs, demonstrations and investigations, in addition to being fundamental to experimental design.

While the original proofs of Hadamard and de la Vallée-Poussin are long and elaborate, and later proofs have introduced various simplifications through the use of Tauberian theorems but remained difficult to digest, a surprisingly short proof was discovered in 1980 by American mathematician Donald J. Newman.

However, its various proofs are non-constructive, as they depend on the law of excluded middle, and therefore rejected by intuitionists.

It borrows directly from the notion of running a program on itself as input, which is also used in various proofs in theoretical computer science, such as the proof that the halting problem is undecidable.

He states the various proofs for the existence of an immaterial, infinite, supreme Being, asserts that this Being is the author of the visible universe, and strongly defends the doctrine of the foreknowledge and particular providence of God.

Specific integers known to be far larger than Graham's number have since appeared in many serious mathematical proofs ( e. g., in connection with Friedman's various finite forms of Kruskal's theorem ).

Their first published proof replaced the cobordism theory of the first proof with K-theory, and they used this to give proofs of various generalizations in the papers.

Since the 1960s, a voluminous literature on the Coase theorem and its various interpretations, proofs, and criticism has developed and continues to grow.

The classes of successor ordinals and limit ordinals ( of various cofinalities ) as well as zero exhaust the entire class of ordinals, so these cases are often used in proofs by transfinite induction or definitions by transfinite recursion.

In that book, the author referred to Commodore Schley as a “ caitiff, poltroon and coward .” The proofs of the book had been read and approved by various naval officers, among them Rear Admiral Sampson.

The theory of probabilistically checkable proofs studies the power of probabilistically checkable proof systems under various restrictions of the parameters ( completeness, soundness, randomness complexity, query complexity, and alphabet size ).

Pascal's original statement and proof of the result differ from those ordinarily seen today, but there are various modern proofs for the theorem.

The numerous quotations from the Qur ' an are not to be regarded as mere ornament, nor even as scriptural proofs adduced in support of various statements.

It borrows directly from the notion of running a program on itself as input, which is also used in various proofs in theoretical computer science, such as the proof that the halting problem is undecidable.

In general relativity, energy conditions are often used ( and required ) in proofs of various important theorems about black holes, such as the no hair theorem or the laws of black hole thermodynamics.

For Hamiltonians that are quadratic at infinity, the Floer homology is the singular homology of the free loop space of M ( proofs of various versions of this statement are due to Viterbo, Salamon – Weber, Abbondandolo – Schwarz, and Cohen ).