He wore tennis shorts and a white sweater with a red V at the neck, the sleeves pushed above the elbows.

Blood dripped down the front of his sweater, soaking into a dark streak of dirt that ran diagonally across the white wool on his shoulder, as though the bright V woven into the neckline had melted, running a darker color.

The battle of the drib-drool continues, but most of New York's knowing sophisticates of Abstract Expressionism are stamping their feet impatiently in expectation of V ( for Vindication ) Day, September first, when Augustus Quasimodo's first one-man show opens at the Guggenheim.

At 100 Amp the 360 cycle ripple was less than 0.5 V ( peak to peak ) with a resistive load.

We are trying to study a linear operator T on the finite-dimensional space V, by decomposing T into a direct sum of operators which are in some sense elementary.

Second, even if the characteristic polynomial factors completely over F into a product of polynomials of degree 1, there may not be enough characteristic vectors for T to span the space V.

On the other hand, the null space of Af and the null space of Af together span V, the former being the subspace spanned by Af and the latter the subspace spanned by Af and Af.

If ( remember this is an assumption ) the minimal polynomial for T decomposes Af where Af are distinct elements of F, then we shall show that the space V is the direct sum of the null spaces of Af.

Let T be a linear operator on the finite-dimensional vector space V over the field F.

Thus the Af are projections which correspond to some direct-sum decomposition of the space V.

Let N be a linear operator on the vector space V.

Let T be a linear operator on the finite-dimensional vector space V over the field F.

Then there is a diagonalizable operator D on V and a nilpotent operator N in V such that ( A ) Af, ( b ) Af.

Let V be a finite-dimensional vector space over an algebraically closed field F, e.g., the field of complex numbers.

Then every linear operator T in V can be written as the sum of a diagonalizable operator D and a nilpotent operator N which commute.

In the primary decomposition theorem, it is not necessary that the vector space V be finite dimensional, nor is it necessary for parts ( A ) and ( B ) that P be the minimal polynomial for T.

Let N be a positive integer and let V be the space of all N times continuously differentiable functions F on the real line which satisfy the differential equation Af where Af are some fixed constants.

If Af denotes the space of N times continuously differentiable functions, then the space V of solutions of this differential equation is a subspace of Af.

If D denotes the differentiation operator and P is the polynomial Af then V is the null space of the operator p (, ), because Af simply says Af.

Let us now regard D as a linear operator on the subspace V.

If we are discussing differentiable complex-valued functions, then Af and V are complex vector spaces, and Af may be any complex numbers.

In the C-plane we construct a set of rectangular Cartesian coordinates u, V with the origin at Q and such that both C and Af have finite slope at Q.

The photocathode sensitivities S, phosphor efficiencies P, and anode potentials V of the individual stages shall be distinguished by means of subscripts 1, and 2, in the text, where required.

The luminous gain of a single stage with Af ( flux gain ) is, to a first approximation, given by the product of the photocathode sensitivity S ( amp / lumen ), the anode potential V ( volts ), and the phosphor conversion efficiency P ( lumen/watt ).

A simple electric circuit, where current is represented by the letter i. The relationship between the voltage ( V ), resistance ( R ), and current ( I ) is V = IR ; this is known as Ohm's Law.

:: Example 2 ( parliamentary republic ): According to Chapter V, Article 60 ( 2 ) of the Basic Law of the Federal Republic of Germany:

According to professor A. V. Dicey in An Introduction to the Study of the Law of the Constitution, the essential features of a federal constitution are: a ) A written supreme constitution in order to prevent disputes between the jurisdictions of the Federal and State authorities ; b ) A distribution of power between the Federal and State governments and c ) A Supreme Court vested with the power to interpret the Constitution and enforce the law of the land remaining independent of both the executive and legislative branches.

* David Raic, Statehood and the Law of Self-Determination ( Developments in International Law, V. 43 ) ( Developments in International Law, V. 43 ), Springer, 2002.

In his seminal Die Grundgesetze der Arithmetik ( Basic Laws of Arithmetic ) he built up arithmetic from a system of logic with a general principle of comprehension, which he called " Basic Law V " ( for concepts F and G, the extension of F equals the extension of G if and only if for all objects a, Fa if and only if Ga ), a principle that he took to be acceptable as part of logic.

Russell discovered that Basic Law V is inconsistent ( this is Russell's paradox ).

They have abandoned Basic Law V in favour of abstraction principles such as Hume's principle ( the number of objects falling under the concept F equals the number of objects falling under the concept G if and only if the extension of F and the extension of G can be put into one-to-one correspondence ).

Frege required Basic Law V to be able to give an explicit definition of the numbers, but all the properties of numbers can be derived from Hume's principle.

In addition, many of the weakened principles that they have had to adopt to replace Basic Law V no longer seem so obviously analytic, and thus purely logical.

The one truly new principle was one he called the Basic Law V: the " value-range " of the function f ( x ) is the same as the " value-range " of the function g ( x ) if and only if ∀ x = g ( x ).

Writing in the American Journal of International Law, professors Jonathan I. Charney and J. R. V. Prescott argued that " none of the post – World War II peace treaties explicitly ceded sovereignty over the covered territories to any specific state or government.

* Timothy V. Waters, On the Legal Construction of Ethnic Cleansing, Paper 951, 2006, University of Mississippi School of Law ( PDF )

Part V of the Law of Property Act 1922 finally extinguished the last of them.

As Henry III had no son, under Salic Law, the next heir to the throne was the Calvinist Prince Henri of Navarre, a descendant of Louis IX whom Pope Sixtus V had excommunicated along with his cousin, Henri Prince de Condé.

The original proposed Federal Marriage Amendment was written by Alliance for Marriage with the assistance of Judge Robert Bork, Professor Robert P. George of Princeton University, and Professor Gerard V. Bradley of Notre Dame Law School.

After the Unionists had failed to win an electoral mandate at either of the General Elections of 1910 ( despite softening the Tariff Reform policy with Balfour's promise of a referendum on food taxes ), the Unionist peers split to allow the Parliament Act to pass the House of Lords, in order to prevent a mass-creation of new Liberal peers by the new King, George V. The exhausted Balfour resigned as party leader after the crisis, and was succeeded in late 1911 by Andrew Bonar Law.

*" William Barclay, Professor of Law at Pont-a-Mousson and Angers " by Andrew F Stewart in Stair Society Miscellany V, ed H L MacQueen, Edinburgh 2006 ISBN 1-872517-18-8

With the Pragmatic Sanction of 1830, Ferdinand set aside the Salic Law, introduced by Philip V, that prohibited women from becoming sovereigns of Spain.

On the coronation of George V on 22 June 1911, Bonar Law was made a Privy Counsellor on the recommendation of the new Prime Minister and Arthur Balfour.