In more ordinary cases Tsar Alexander III could be at once kind, simple, and even almost homely.

Hence the expression praeteriti senatores (" senators passed over ") is equivalent to e senatu ejecti ( those removed from the senate ).</ br > In some cases, however, the censors did not acquiesce to this simple mode of proceeding, but addressed the senator whom they had noted, and publicly reprimanded him for his conduct.

In such cases variables are represented through vectors instead of simple scalar values.

For example, the Cyrillic letter Р is usually written as R in the Latin script, although in many cases it is not as simple as a one-for-one equivalence.

The first case was done by the Gorenstein – Walter theorem which showed that the only simple groups are isomorphic to L < sub > 2 </ sub >( q ) for q odd or A < sub > 7 </ sub >, the second and third cases were done by the Alperin – Brauer – Gorenstein theorem which implies that the only simple groups are isomorphic to L < sub > 3 </ sub >( q ) or U < sub > 3 </ sub >( q ) for q odd or M < sub > 11 </ sub >, and the last case was done by Lyons who showed that U < sub > 3 </ sub >( 4 ) is the only simple possibility.

In most cases, cholera can be successfully treated with oral rehydration therapy ( ORT ), which is highly effective, safe, and simple to administer.

Financial losses are usually simple to quantify but in complex cases which involve loss of pension entitlements and future loss projections, the instructing solicitor will usually employ a specialist expert actuary or accountant to assist with the quantification of the loss.

The following examples show how to solve differential equations in a few simple cases when an exact solution exists.

In both cases, a distinction is made between simple and complex ideas.

They hear the most simple of criminal cases ( or sit when the Senior Magistrate is not in the Islands ) and they also act as the Licensing Justices who deal with alcohol-related applications, such as extended opening hours, special occasion licences, etc.

The SM is resident in the Islands and hears the majority of cases from simple criminal and civil matters right up to very serious criminal matters or complex civil cases.

As in the simple cases above, one may enumerate all distinct four-colorings of the ring ; any coloring that can be extended without modification to a coloring of the configuration is called initially good.

In all cases, however, sharia ( Islamic religious law ) calls for burial of the body, preceded by a simple ritual involving bathing and shrouding the body, followed by salah ( prayer ).

It generally consists of a series of simple and in some cases, potentially life-saving techniques that an individual can be trained to perform with minimal equipment.

However, his work for the Sistine Chapel is descended from the Palestrina style, and in some cases strips even this refined, simple style of all ornament.

However, while this simple correspondence between an allele and a trait works in some cases, most traits are more complex and are controlled by multiple interacting genes within and among organisms.

The Ebers papyrus also provides our earliest possible documentation of ancient awareness of tumors, but ancient medical terminology being badly understood, cases Ebers 546 and 547 for instance may refer to simple swellings.

For simple systems, where the interrupts were not used, it is possible to find cases where this pin is used as an additional single-bit output port ( the popular Radio86RK computer made in the former Soviet Union, for instance ).

In very simple cases, knitting can be done without tools, using only the fingers to do these tasks ; however, knitting is usually carried out using tools such as knitting needles, knitting machines or rigid frames.

Methods of bivariate statistics, for example simple linear regression and correlation, are NOT special cases of multivariate statistics because only one outcome variable is involved.

Even cases considered " regular ", with the final-s, are not so simple ; the-s in dogs is not pronounced the same way as the-s in cats, and in a plural like dishes, an " extra " vowel appears before the-s. These cases, where the same distinction is effected by alternative forms of a " word ", are called allomorphy.

An important microstructural feature of a polymer is its architecture, which relates to the way branch points lead to a deviation from a simple linear chain.

It relates in simple Greek language what the Church experienced from the days of Constantine to the writer's time.

To see how the binomial theorem relates to the simple construction of Pascal's triangle, consider the problem of calculating the coefficients of the expansion of ( x + 1 )< sup > n + 1 </ sup > in terms of the corresponding coefficients of ( x + 1 )< sup > n </ sup > ( setting y

Like the apologue, the parable generally relates a single, simple, consistent action, without a great deal of circumstantial detail.

The first relates to the phenomenon that a scribe, when copying a text, will tend to converge on his source out of simple fatigue.

A simple general circulation model ( SGCM ), a minimal GCM, consists of a dynamical core that relates material properties such as temperature to dynamical properties such as pressure and velocity.

The Panegyric of Maximian, dating to 289 and attributed to Claudius Mamertinus, relates that during the bagaudae uprisings of 284 – 285 in the districts around Lugdunum ( Lyon ), " simple farmers sought military garb ; the plowman imitated the infantryman, the shepherd the cavalryman, the rustic harvester of his own crops the barbarian enemy ".

It is, however, avoided in the scientific press, as it relates to the concept of the great chain of being and to the notion of simple organisms being primitive versions of complex ones, both of which have been discarded in biology.

Jesus ' parables are seemingly simple and memorable stories, often with imagery, and each conveys a teaching which usually relates the physical world to the spiritual world.

This relates to the simple fact that business knowledge is highly tentative, and subject to error or obsolescence.

* A simple explanation of hull speed as it relates to heavy and light displacement hulls

: More specifically, this invention relates to a four barrel break-open firearm which has a minimum number of working parts, is simple to operate even by inexperienced personnel, and is economical to manufacture.

They seem certain that at least one of them " Muntakhabul Kalam ..." is definitely non-genuine, for the simple reason that it relates those stories that happened long after Sirin's death as already stated.

The chief influence at work here seems to have been the idea of the celestial Anthropos ( i. e. the Primal Man ) – of whom the myth originally relates that he has sunk into matter and then raised himself up from it again – which appears in its simple form in individual Gnostic systems, e. g. in Poimandres ( in the Corpus Hermeticum ) and in Manichaeism.

The simple equation which relates power, voltage and frequency above also does not take into account the static power consumption of the CPU.

The IQR is used to build box plots, simple graphical representations of a probability distribution.

This can be used to reduce some problems about Lie groups ( such as finding their unitary representations ) to the same problems for connected simple groups and nilpotent and solvable subgroups of smaller dimension.

If k is a field and G is a group, then a group representation of G is a left module over the group ring k. The simple k modules are also known as irreducible representations.

Digital electronic circuits are usually made from large assemblies of logic gates, simple electronic representations of Boolean logic functions.

The main property that makes these genetic representations convenient is that their parts are easily aligned due to their fixed size, which facilitates simple crossover operations.

This follows from other, less simple ( but very interesting ) representations of the knot:

These representations can be as simple as an on-screen traffic light, which represents the state of an actual traffic light in the field, or as complex as a multi-projector display representing the position of all of the elevators in a skyscraper or all of the trains on a railway.

Over time, the stelae changed from simple representation of figures, such as Monument 19 or La Venta Stela 1, toward representations of historical events, particularly acts legitimizing rulers.

Curves, or at least their graphical representations, are simple to create, for example by a stick in the sand on a beach.

As a result, when society evolves and looks back to these representations, it considers its own present as the decline of the simple life of the past.

Mathematical notations include relatively simple symbolic representations, such as the numbers 0, 1 and 2, function symbols sin and +; conceptual symbols, such as lim, dy / dx, equations and variables ; and complex diagrammatic notations such as Penrose graphical notation and Coxeter-Dynkin diagrams.

Although it has been believed that simple implementations of top-down parsing cannot accommodate direct and indirect left-recursion and may require exponential time and space complexity while parsing ambiguous context-free grammars, more sophisticated algorithms for top-down parsing have been created by Frost, Hafiz, and Callaghan which accommodate ambiguity and left recursion in polynomial time and which generate polynomial-size representations of the potentially exponential number of parse trees.

Briefly, finite-dimensional representations of a semisimple Lie algebra are completely reducible, so it suffices to classify irreducible ( simple ) representations.

* Transforming digitized representations of objects, for example ( A ) into simplified shapes such as ( i ) skeletons, by repeated removal of simple points such that the digital topology of an image does not change, or ( ii ) medial axis, by calculating local maxima in a distance transform of the given digitized object representation, or ( B ) into modified shapes using mathematical morphology.

They discovered how to fit the gauge forces in the standard model into an SU ( 5 ) group, and the quarks and leptons into two simple representations.

Some decision tables use simple true / false values to represent the alternatives to a condition ( akin to if-then-else ), other tables may use numbered alternatives ( akin to switch-case ), and some tables even use fuzzy logic or probabilistic representations for condition alternatives.

As a consequence, there are many finite-dimensional representations which are all built out of simple representations of dimension p.

Real and pseudoreal representations of a group G can be understood by viewing them as representations of the real group algebra R. Such a representation will be a direct sum of central simple R-algebras, which, by the Artin-Wedderburn theorem, must be matrix algebras over the real numbers or the quaternions.

Among the compact real forms of the simple Lie groups, irreducible quaternionic representations only exist for the Lie groups of type A < sub > 4k + 1 </ sub >, B < sub > 4k + 1 </ sub >, B < sub > 4k + 2 </ sub >, C < sub > k </ sub >, D < sub > 4k + 2 </ sub >, and E < sub > 7 </ sub >.

The framework is a simple and logical structure for classifying and organizing the descriptive representations of an enterprise.

These studies showed how the visual system builds an image from simple stimuli into more complex representations.