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	Computer Science: The Search for a Mathematical Theory
		Thus formal logic is, by the nature of its approach, cut off from the best cultivated portions of mathematics, and forced onto the most difficult part of the mathematical terrain, into combinatorics.
		Their formalism, aimed at retaining the flavor of the machine and its ties to Turing machines, became the standard for the field, beginning, significantly, with tapes formed by finite sequences of symbols from a finite alphabet.
		Far from merely complementing the study of computer science, the subject of automata and formal languages became the theoretical core of the curriculum during the 1970s, especially as it was embedded in such tools as lexical analyzers and parser generators.
	www.princeton.edu /~mike/articles/20thcSci/20thcent.html (7971 words)

	SSR 61-55
		Formal filing did not occur within the succeeding 2-year period but the claimant is deemed to have filed application within this latter period when he mailed the above letter requesting payment of the lump sum and he may be found to be entitled to the lump-sum death payment on the basis of the application filed.
		Although the formal application for a lump-sum death payment was executed and filed by R on March 20, 1961, more than 4 years after the worker's death, R's letter of January 20, 1961, was received by the Administration less than 4 years after the worker's death.
		Also, the formal application was filed within 6 months from the date thereafter that the Bureau notified him that an application on a prescribed form was necessary.
	www.ssa.gov /OP_Home/rulings/oasi/17/SSR61-55-oasi-17.html (779 words)

	Differential Forms and the Generalized Stokes Theorem
		Roughly, a vector space is a set of entities such that the sum of any vectors is also a vector and the result of multiplying a vector by a scalar is also a vector.
		Formally the vector space is a set of four things, (V,k,+,) where V is the set of vectors, K is the field of scalars involved in creating multiples of vectors, + is the function involved in adding two vectors and * is the binary function involved in multiplying a vector by a scalar.
		Roughly a k-form is the formal sum of functions over the space f*(P) times the basic k-forms.
	www.sjsu.edu /faculty/watkins/difforms.htm (1932 words)

	Home
		Sum's automatic ergonomics and slender profile provide sophistication and comfort.
		Sum conforms and adjusts automatically, providing support and comfort right where it's needed.
		Sum's automatic ergonomics allow anyone to be instantly comfortable and focused.
	www.allsteeloffice.com (0 words)

	[No title]
		An expression that occurs in a generic formal part is either the default expression for a generic formal object of mode in, or a constituent of an entry name given as default name for a formal subprogram, or the default expression for a parameter of a formal subprogram.
		The type of a generic formal object of mode in must not be a limited type; the subtype of such a generic formal object is the subtype denoted by the type mark given in the generic parameter declaration.
		The instance is a copy of the generic unit, apart from the generic formal part; thus the instance of a generic package is a package, that of a generic procedure is a procedure, and that of a generic function is a function.
	www.csci.csusb.edu /dick/cs320/ada/lrm/12.generics (3312 words)

	Kids.Net.Au - Encyclopedia > Formal power series (Site not responding. Last check: )
		Formal power series are devices in mathematics that make it possible to employ much of the analytical machinery of power series in settings that do not have natural notions of "convergence".
		Formal power series can also be interpreted as functions, but one has to be careful with the domain and codomain.
		The formal derivative has many of the properties of the continuous derivative of calculus.
	www.kids.net.au /encyclopedia-wiki/fo/Formal_power_series (1454 words)

	[No title] (Site not responding. Last check: )
		Formal parameters are like local variables for the function and may have the same names as formal parameters or local variables for other functions.
		In this case TPL converts the values to the correct type for the formal parameters on entry to the function and converts the value of the formal parameters on exit to the type of the argument variables as the values are passed back.
		Because of this, the number of columns and rows specified for the formal parameter array are ignored and you may specify 0 to emphasize that the size is dependent on the passed array.
	www.sandh.com /snhnew/manuals/tpl05.HTM (1451 words)

	Formal-Numeric Series (Site not responding. Last check: )
		It's interesting to consider formal associations of different numerical series with each other according to their partial sums rather than according to their terms.
		Specifying the partial sums implies an ordering that removes infinitely many degrees of freedom from the evaluation of a series.
		In general, since the nth partial sum of the natural sequence is n(n+1)/2, and the mth partial sum of the geometric sequence 1 + b + b^2 +...
	www.mathpages.com /home/kmath500.htm (448 words)

	Chain (mathematics)
		In algebraic topology, a simplicial k-chain is a formal linear combination of k-simplices.
		Example 2: The boundary of the triangle is a formal sum of its edges with signs arranged to make the traversal of the boundary counterclockwise.
		Example 3: A 0-cycle is a linear combination of points such that the sum of all the coefficients is 0.
	www.ebroadcast.com.au /lookup/encyclopedia/ch/Chain_(mathematics).html (261 words)

	Chapter 16. Summary of Mathematical Results (Site not responding. Last check: )
		Because the rules are informal, it is necessary to provide a separate, formal derivation of the results as a double-check of their validity.
		As stated previously, the formal derivation has already been done, and is printed in Appendix A.
		The formal results are close to the informal results on all points.
	mbdefault.org /16_summary/default.asp (929 words)

	Singular homology - Biocrawler (Site not responding. Last check: )
		Singular homology is constructed by applying the general homology construction to the singular chain complex, the chain complex of formal sums of singular simplices.
		The boundary of σ, dσ, is defined to be the formal sum of the singular (n−1)-simplices represented by the restriction of σ to the faces of the standard n-simplex, with an alternating sign to take orientation into account.
		If we consider the free abelian groups generated by all singular n-simplices and extend the boundary operator d to formal sums of singular n-simplices, we obtain a chain complex of abelian groups.
	www.biocrawler.com /encyclopedia/Singular_homology (257 words)

	Math Forum - Ask Dr. Math
		One, which we might call a "formal sum" since the focus is on the form, is for an EXPRESSION such as 3 + 4 which shows some number of terms being added.
		When we define a series as the (formal) sum of consecutive terms, we are thinking of the form, not the value: a1 + a2 + a3 +...
		In the case of an infinite series, the sum of the series must be expressed as a limit of partial sums, so the evaluation process is different, but the distinction is the same.
	www.mathforum.com /library/drmath/view/65799.html (382 words)

	Summary: Rehabilitating the Benjamin Franklin Parkway
		However, as also illustrated by this case study, when addressing a formal feature such as a linear parkway or boulevard, a phased approach is usually not successful in creating the visual and spatial organization of the historic design in the future.
		The result of partial removals in a formal feature is a radical change in the character and appearance from the historic period to the present day - - and thus never achieves the original design intent.
		In sum, the coupling of thorough documentation of history and existing conditions with a broadly conceived public outreach program led to public consensus for this rehabilitation treatment.
	www.cr.nps.gov /hps/hli/currents/franklinpark/summary.htm (338 words)

	ROCO Chapter 1: Drawing Method 1
		Formal charges show whether a Lewis structure assigns too few or too many electrons to an atom.
		They are called "formal" because they are derived using rules that may, or may not, reflect an atom's true electrical properties.
		Formal charges are calculated by considering the number of electrons "held" by an atom at any given moment, and not the total number of electrons "seen" by the atom.
	academic.reed.edu /chemistry/ROCO/Lewis/drawing_1.html (615 words)

	Chapter Six
		Overall, formal diversion programs are concentrated most heavily in states in the west and south; very few states in the northeast have established these formal diversion programs.
		In contrast to lump sum payments that are guided by a relatively complex set of policies and procedures, the process of linking applicants with alternative resources occurs primarily on a case by case basis through a one-on-one interaction between a caseworker and the applicant.
		Although these conversations primarily focused on lump sum payment programs as the most structurally formal of these diversion activities, their comments were sufficient to provide a general sense about data collection and data issues.
	aspe.hhs.gov /hsp/isp/diverzn/chptsix.htm (3020 words)

	QuaSAR-Descriptor (Site not responding. Last check: )
		Sum of the absolute value of the difference between atomic polarizabilities of all bonded atoms in the molecule (including implicit hydrogens) with polarizabilities taken from [CRC 1994].
		Approximation to the sum of VDW surface areas of pure hydrogen bond acceptors (not counting acidic atoms and atoms that are both hydrogen bond donors and acceptors such as -OH).
		Approximation to the sum of VDW surface areas of pure hydrogen bond donors (not counting basic atoms and atoms that are both hydrogen bond donors and acceptors such as -OH).
	www.chemcomp.com /Journal_of_CCG/Features/descr.htm (4166 words)

	Formal Charge (Site not responding. Last check: )
		The formal charge on an atom is the number of valence electrons on the free (nonbonded) atom minus the number of electrons assigned to that atom in the Lewis structure.
		Note that the sum of the formal charges on all the atoms in a molecule will be zero while for an ion it will be equal to the charge on the ion.
		Formal charges on the atoms in a Lewis structure must total to zero for a molecule and to the net charge for a polyatomic ion.
	chemistry.twu.edu /tutorial/FormalChargeSum.html (383 words)

	Euclidean geometry - RecipeFacts (Site not responding. Last check: )
		If two lines intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough.
		Formal mereology began only in 1916, with the work of Lesniewski and A.
		In hyperbolic geometry the sum of the three angles are always less than 180° and can approach zero, while in elliptic geometry the sum is greater than 180°.
	www.recipeland.com /facts/Euclidean_geometry (2180 words)

	tScholars.com \| Divisor (algebraic geometry) (Site not responding. Last check: )
		In the classical theory, where locally finite is automatic, the group of Weil divisors on a variety of dimension n is therefore the free abelian group on the (irreducible) subvarieties of dimension (n − 1).
		For example, a divisor on an algebraic curve is a formal sum of its points.
		An effective Weil divisor is then one in which all the coefficients of the formal sum are non-negative.
	www.tscholars.com /encyclopedia/Weil_divisor (424 words)

	PlanetMath: simplicial complex
		Although there is an established notion of infinite simplicial complexes, the geometrical treatment of simplicial complexes is much simpler in the finite case and so for now we will assume that
		and the vector space operations are defined by formal addition and scalar multiplication.
		as a one-term formal sum, and thus as a point in
	planetmath.org /encyclopedia/SimplicialComplex.html (473 words)

	A brief history of lending and financing in the United States
		The history of formal lending in the United States, as opposed to other sorts, is deeply entwined with the rise of home ownership in the lower socio-economic classes.
		Formal lending, in terms of institutional lending, has long been the means by which many have been able to buy their own home.
		The balloon payment, a large lump sum due at the end of the repayment schedule, was a feature of the typical lending terms.
	www.directlendingsolutions.com /history_of_lending.htm (0 words)

	Topics (Site not responding. Last check: )
		Another rule that is very important to bear in mind is that the sum of formal charges of the Lewis structure of a molecule or ion must be equal to the net charge on the molecule or ion.
		If this is not the case, there is a mistake either in the formal charge assignments or in the Lewis structure (probably the wrong number of valence electrons).
		Although we can easily calculate formal charge according to the formula above, it is helpful to be able to recognize patterns for selected elements.
	guweb2.gonzaga.edu /faculty/cronk/chemistry/resources.cfm?resource=topics&topic=formal-charge (215 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal (Site not responding. Last check: )
		The formal oxidation state is the hypothetical charge that an atom would have if all bonds to atoms of different elements were 100% ionic.
		Formal oxidation states require particular caution for molecules where the bonding is covalent, since the formal oxidation states require the heterolytic removal of ligands, which essentially denies covalency.
		The algebraic sum of oxidation states of all atoms in a neutral molecule must be zero, while in ions the algebraic sum of the oxidation states of the constituent atoms must be equal to the charge on the ion.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=oxidation_state (935 words)

	Introduction to Bonding
		The situation in which both atoms have formal charges of zero is better (reflects a more stable molecule) than the situation in which one has a -1 formal charge and the other has a +1 formal charge.
		Note that sum of the formal charges in a molecule will be equal to zero, since all of the electrons are assigned and counted.
		The sum of the four formal charges is still -2, but now two of the four atoms have formal charges of zero.
	www.chemprofessor.com /bonding.htm (3534 words)

	Bonus, Incentive and Non-monetary Awards \| Policies for All Staff at Indiana University \| UHRS
		Formal recognition programs including lump-sum bonuses, incentive plans and non-monetary awards offer mechanisms to effectively motivate and retain valued employees who provide exemplary performance and/or meet specified targets.
		These programs are intended to reward staff employees whose achievements have resulted in a particular benefit to the department, the campus, and/or Indiana University.
		All staff employees, including teams and partnerships of such employees, are eligible to participate.
	www.indiana.edu /~uhrs/policies/appointed/bonus.html (1134 words)

	Definitions Country Codes geographic.org Courty Profiles - Flags, Maps, Economy, Geography, Climate, Natural Resources, ...
		Total area is the sum of all land and water areas delimited by international boundaries and/or coastlines.
		Water area is the sum of all water surfaces delimited by international boundaries and/or coastlines, including inland water bodies (lakes, reservoirs, rivers).
		Formal commitments of aid are included in the data.
	www.theodora.com /wfb/wfb2000/definitions.html (12538 words)

	Adherents.com: Largest Religious Bodies
		Some religious bodies are mostly regional but are not part of a broader formal global communion representing their movement precisely: the great majority of their branches are located in a limited region, and there are no separate "sister churches" in other parts of the world.
		Furthermore, many religionists may have no formal organizational membership or denominational identity other than as a resident of the culture, tribe or country into which they were born.
		The sum membership of only these, the "world's largest religious bodies" (over 120 bodies are on this list) account for about 47.4% of the world's population.
	www.adherents.com /adh_rb.html (5270 words)

	Genetic Epistemology
		But although we recognise the importance of formalisation in epistemology, we also realize that formalisation cannot be sufficient by itself.
		The third reason why formalisation is not enough is that epistemology sets out to explain knowledge as it actually is within the areas of science, and this knowledge is, in fact not purely formal: there are other aspects to it.
		Moreover, the sum was not in the pebbles themselves; it was he who united them.
	www.marxists.org /reference/subject/philosophy/works/fr/piaget.htm (4839 words)

	Karl Popper (Stanford Encyclopedia of Philosophy)
		On the quantitative account, verisimilitude is defined by assigning quantities to contents, where the index of the content of a given theory is its logical improbability (given again that content and probability vary inversely).
		Formally, then, Popper defines the quantitative verisimilitude which a statement ‘a’ possesses by means of a formula:
		For these reasons, the deficiencies discovered by the critics in Popper's formal definitions were seen by many as devastating, precisely because the most significant of these related to the levels of verisimilitude of false theories.
	plato.stanford.edu /entries/popper (8080 words)

	Differential Forms and the Generalized Stokes Theorem
		Roughly, a vector space is a set of entities such that the sum of any vectors is also a vector and the result of multiplying a vector by a scalar is also a vector.
		Formally the vector space is a set of four things, (V,k,+,) where V is the set of vectors, K is the field of scalars involved in creating multiples of vectors, + is the function involved in adding two vectors and * is the binary function involved in multiplying a vector by a scalar.
		Roughly a k-form is the formal sum of functions over the space f*(P) times the basic k-forms.
	www2.sjsu.edu /faculty/watkins/difforms.htm (0 words)

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