Generating Sentence Examples

The latter is therefore called the generating function of the former.

Putting n equal to co, in a generating function obtained above, we find that the function, which enumerates the asyzvgetic seminvariants of degree 0, is 1 1-z2.1-z3.1-z4....1-z0 that is to say, of the weight w, we have one form corresponding to each non-unitary partition of w into the parts 2, 3, 4,...0.

The generating function is I - z2' 52 For 0 =3, (alai +a2a2+a3a3) 10; the condition is clearly a1a2a3 = A3 = 0, and since every seminvariant, of proper degree 3, is associated, as coefficient, with a product containing A3, all such are perpetuants.

The generating function is thus z2e-1 - 1 (1 -z 2) (1 -z 3) (1 -z 4)...

Their Number For Any Weight W Is The Number Of Ways Of Composing W 3 With The Parts I, 2, And Thus The Generating Function Is Verified.

By the rules adopted we take A?B 2 B 3, which gives (12)a(32)b - (1)a(321)b+ao(3212)b, the simplest perpetuant of weight 7; and thence the general form enumerated by the generating function 1 -z.1-z2.1 - z3 ?

If a longitudinally magnetized wire is twisted, circular magnetization is developed; this is evidenced by the transient electromotive force induced in the iron, generating a current which will deflect a galvanometer connected with the two ends of the wire.

Laplace published in 1779 the method of generating functions, the foundation of his theory of probabilities, and the first part of his Theorie analytique is devoted to the exposition of its principles, which in their simplest form consist in treating the successive values of any function as the coefficients in the expansion of another function with reference to a different variable.

A direct and an inverse calculus is thus created, the object of the former being to determine the coefficients from the generating function, of the latter to discover the generating function from the coefficients.

In the same way, the generating function of the series I+2x+x 2 +0.x 3 +o.x 4 +...

Then let a small, very short cylinder be described of which dS is a section, and the generating lines are normal to the surface.

Then since the generating lines of the tube are lines of force, the component of the electric force perpendicular to the curved surface of the tube is everywhere zero.

These can, however, only be used advantageously where there are fixed pumps, the fall of water generating the power resulting in a load to be removed by the expenditure of an equivalent amount of power in the pumping engine above that necessary for keeping down the mine water.

Notable examples are found in the Rateau, Ser and Capell fans, and where an electric generating station is available electric motors can be advantageously used instead of steam.

Motion is obtained from a continuous-current generator driven by an alternating motor with a very heavy fly-wheel, a combination known as the Ilgner transformer, which runs continuously with a constant draught on the generating station, the extremely variable demand of the winding engine during the acceleration period being met by the energy stored in the fly-wheel, which runs at a very high speed.

The subject received little attention in the United Kingdom, owing to the relatively high cost of home-produced alcohol as compared with that of imported petrol; and the use of alcohol in England for generating mechanical power was neither contemplated nor provided for by the Legislature before 1920, when, as the result of the consideration of the position by the Government, following on a report by a Departmental Committee appointed towards the end of 1918, clauses were inserted in the Finance Act of 1920 legalizing the use of alcohol for power purposes.

It sprang into importance through the utilization of the falls in the river Glommen for driving saw-mills and generating electric power.

We have for the number of partitions an analytical theory depending on generating functions; thus for the partitions of a number n with the parts I, 2, 3, 4, 5, &c., without repetitions, writing down the product I +x.

And so in other cases we obtain a generating function.

The city has a large jobbing trade, a coal supply from rich deposits in Pierce county, and abundant water-power from swift mountain streams, which is used for generating electricity for municipal and industrial use.

This last point is important in connexion with voltmeters used on the switchboards of electric generating stations, where relatively strong electric or magnetic fields may be present, due to strong currents passing through conductors near or on the board.

The great extension during the same period of the use of water-power has been of immense importance to Canada, most of the provinces possessing numerous swift-flowing streams or waterfalls, capable of generating a practically unlimited supply of power.

From this point of view, the function which, by algebraical operations on i+o.x+o.x2+..., produces the series, is called its generating function.

In drilling for some of the first oil wells gas escaped, and in a few instances this was used as a fuel for generating steam in the boilers of the drilling-engines.

Knowing this, and having in the Siemens regenerative gas furnace an independent means of generating this temperature, the Martin brothers of Sireuil in France in 1864 developed the open-hearth process of making steel of any desired carbon-content by melting together in this furnace cast and wrought iron.

The oxidation of manganese is capable of generating a very high temperature, but it has the very serious disadvantage of causing such thick clouds of smoky oxide of manganese as to hide the flame from the blower, and prevent him from recognizing the moment when the blow should be ended.

A pair of electric arcs play between these electrodes and the molten steel, passing through the layer of slag, G, and generating much heat.

The; line which, winding round an axis either to the right or to the left, passes through the points of insertion of all the leaves on the axis is termed the genetic or generating spiral; and that margin of each leaf which is towards the direction from which the spiral proceeds is the kathodic side, the other margin facing the point whither the spiral passes being the anodic side.

In cases where the internodes are very short and the leaves are closely applied to each other, as in the house-leek, it is difficult to trace the generating spiral.

The primitive or generating spiral may pass either from right to left or from left to right.

Teeth of Skew-Bevel Wheels.The crests of the teeth of a skew-bevel wheel are parallel to the generating straight line of the hyperboloidal pitch-surface; and the transverse sections of the teeth at a given pitch-circle are similar to those of the teeth of a bevelwheel whose pitch surface is a cone touching the hyperboloidal surface at the given circle.

But it was not until the dynamo was improved as a machine for generating large quantities of electricity at a very low cost that the electrolysis of copper could be practised on a commercial scale.

If we suppose these generating lines to be normal to the plane of the paper, then all sections of the solids parallel to this plane will be equal and similar to each other, and the section of the surface of the liquid will be of the same form for all such sections.

The condition of stability of a catenoid is therefore that the tangents at the extremities of its generating catenary must intersect before they reach the directrix.

Galileo attempted the evaluation by weighing the curve against the generating circle; this rough method gave only an approximate value, viz., a little less than thrice the generating circle.

The cartesian equation in terms similar to those used above is x = a6+b sin 0; y=a-b cos 0, where a is the radius of the generating circle and b the distance of the carried point from the centre of the circle.

The river Pescara and its tributary the Tirino form an important source of power for generating electricity.

Such a curve may be considered as described by a point, moving in a line which at the same time rotates about the point in a plane which at the same time rotates about the line; the point is a point, the line a tangent, and the plane an osculating plane, of the curve; moreover the line is a generating line, and the plane a tangent plane, of a developable surface or torse, having the curve for its edge of regression.

The section made by a plane containing the axis and perpendicular to the base is a triangle contained by two generating lines of the cone and a diameter of the basal circle.

A method of generating conics essentially the same as our modern method of homographic pencils was discussed by Jan de Witt in his Elementa linearum curvarum (1650); but he treated the curves by the Cartesian method, and not synthetically.

The penstock, three feet in diameter at this point, was a long black snake, carrying its mountain water to the small generating station, while adjacent black piping and frequent taps provided the ice that coated the cliff sides in gigantic clusters below.

Find out more... Media Relations A strong Internet presence is a proven tool for generating additional PR for your company.

While linear methods have proven invaluable over many years in generating first-order approximations, they are severely limited in both qualitative and quantitative predictions.

Waste paper, not included in this chart, is also a good substrate for generating biogas.

Generating f0 contours for speech synthesis using the tilt intonation theory.

Finally, I totally agree with Bond that discourse contexts will improve generating more accurate determiners that have anaphoric relations.

Genomixer the Future Physical funded project made serious progress and uses stanza DNA data fused into online generating artworks and soundscapes.

Research focussed on methods of generating and stabilizing emulsion droplets using cross-linked polymer coatings derivatised with various ligands.

These magazines are there simply to sell advertising, they are profit generating publications not educational or philanthropic publications.

We specialize in design, installation, servicing and maintenance of diesel powered generating units and ancillary equipment.

Above all, how does one actually go about generating successful firesides?

Fitted with exclusive 100% low torque graphite shafts generating high club head speed.

In this article, we describe an approach to generating peptide maps by limited acid hydrolysis.

The basement of the mill contains a watercourse which is perfect for modern micro hydropower technology capable of generating green electricity.

Assets play a crucial role in generating Britain's widening inequality.

We were also very successful in generating a significant cash inflow which benefits the whole Group.

The Sales Executive for this role will be in charge of generating advertising revenue for this leading ISP.

Spread with a circular motion generating a fine, rich lather.

At that time, the landfill site at Buckden in Cambridgeshire was generating leachate containing significant concentrations of herbicides, mecoprop and isoproturon.

Logging of interesting packets logging of interesting packets Logging must be done for only a few packets that are deemed interesting, to avoid generating lots of noise.

You will assist the business by generating sales opportunities using proactive approach telemarketing, direct mail and email marketing, direct mail and email marketing.

The property GROUP is responsible for generating income from the sale or rent of property owned by the city council.

Random Dance is committed to developing extensive participatory and outreach opportunities and generating new work for and by young people.

The weirdest formulas for generating primes that I've come across are these.

They ranged from collusion with state and regularity authorities, generating favorable publicity about the safety of its products, and even espionage.

This work involves studies of the Hybrid Monte Carlo algorithm for generating dynamical quarks.

At that point, we will explain how to use self-service for generating cover sheets.

The sector exported £ 14.2 billion in 1994, generating a trade surplus of £ 2.6 billion.

The emphasis seems to be more on embracing current trends than generating suspense.

Investigation of the neuronal aggregate generating seizures in the rat tetanus toxin model of epilepsy.

Even if one of the generating stations fails, the system copes and is virtually unaffected.

Whilst some such classifications may be fairly unequivocal, generating useful schema is an ongoing task.

The Gilkes Vortex turbine was manufactured in Kendal and drove a 6kw dynamo generating 110 volts.

These two lines may be pictured in the in solido definition as the section of a cone by a plane through its vertex and parallel to the plane generating the hyperbola.

The doctrine of Anaximenes, who unites the conceptions of a determinate and indeterminate original substance adopted by Thales and Anaximander in the hypothesis of a primordial and all-generating air, is a clear advance on these theories, inasmuch as it introduces the scientific idea of condensation and rarefaction as the great generating or transforming agencies.

A comparison with another method of generating the interface, similar to that previously employed when but one body was in question, will now allow us to evaluate T12.

The form of the surface of a liquid acted on by gravity is easily determined if we assume that near the part considered the line of contact of the surface of the liquid with that of the solid bounding it is straight and horizontal, as it is when the solids which constrain the liquid are bounded by surfaces formed by horizontal and parallel generating lines.

The company is working with communities in several villages affected, helping develop proposals for income generating projects and administering small pump priming grants.

Generating reagents to unknown and hypothetical receptors that have been identified using our mass spectrometry based approach.

All our revenue generating products will help to ensure the sustainability of the free public website.

Both of these schizont stages release numerous merozoites, capable of infecting erythrocytes and generating the bloodstream forms of the parasite.

Giles Ponsford was not only stager manager and actor but also a madcap schemer in generating audiences for his show.

Polycyclic Groups Finite soluble groups and infinite polycyclic groups have special generating systems chosen in accordance with a subnormal series with cyclic factors.

The kinase phosphorylates the CDKs on a threonine residue which lies within the activation segment, a modification essential for generating kinase activity.

At the same time, the protein pumps protons across the membrane generating a transmembrane gradient.

The function is great for generating valid XHTML and semantic code from database content.

Hopefully, the synergy of our combined teams are generating will have effective results for the struggling businesses.

Another idea is to make small booklets of these memories by taking them to a printer or generating them yourself using a word processing program on a computer.

Cradle cap is a condition marked by overactive sebaceous glands that are generating too much sebum.

Many of these products contain silica. which is also generating its fair share of controversy.

Generating a number requires a sophisticated algorithm.

The light generated by the newer CFLs is of a higher quality than it used to be, generating a warmer light.

Less waste - Recycling is great, but using plastic and glass bottles (even better because plastic is a petroleum by product) is even better because you aren't generating any new waste by buying new products.

Turbine blades turn in several parts of the country, generating power from the wind currents that flow across the Earth as a direct result of the uneven heating of the planet as it orbits the sun.

Petroleum, also known as crude oil, is used for generating electricity and for manufacturing.

The use of fossil fuels, dams and other environmentally harmful methods of generating power grew exponentially during this century, but so did the science behind solar power.

The smallest wind turbines which are capable of generating 20-500 watt units are used for things like charging batteries for sailboats and other small, recreational applications.

Generating enough energy from wind alone to power a factory or a whole city is still unrealistic.

Generating electricity from wind is a simple process.

Generating energy from renewable sources can work out as a very economical option over time.

It can sometimes be very easy to think that going green involves being completely self sufficient, living off grid, generating your own energy, growing your own food and only using a bicycle for transportation.

A lot of space is required for growing and rearing food, generating energy and other essentials, as well as for normal living space.

It beginsby making good choices, such asbuying in bulk to avoid generating more waste.

Even Hallmark and American Greeting, two of the top greeting card companies, now offer free greeting cards as a method of promotion and generating advertising revenue.

When the online community first became a viable venue for generating significant retail sales, most online stores charged customers for shipping costs.

Microstock photo agencies cater to novice photographers who are passionate about taking pictures, want to share their work with others, and are interested in generating cash from the process.

It releases endorphins, takes the mind off problems that may be generating stress and leaves a positive outlook in its wake.

Paula is especially interested in "generating visual composition and expression," which includes film, photography, painting and sculpture.

Their romance began generating media attention around Chrismas 2003.

Always work in a well-ventilated area if you are using adhesives or generating sawdust.

Good for earth" is generating tremendous appeal at the grab-and-go moment.

The clothing is made and sold as a way of generating income for assistance and training programs for women that have experienced trauma, violence or poverty.

The best method of treatment is through prevention and generating public awareness through widespread education on the topic.

It should be noted that Rosetta Stone's first product lines were not so much geared toward the academic community, but more toward generating fluency.

Alternately, the co-borrowers could keep the home and transition it to income generating rental property.

Other styles generating a lot of sales and interest are "Femme Fatale,", "Bling" and "Flora".

Fortunately, the tankini has been generating a lot of attention over the last five years and now swim boutiques and department stores have racks full of these modest, yet, potentially sexy swimsuits.

The recommended daily allowance focuses on preventing deficiency as opposed to generating optimum health, and additional vitamin C may be beneficial.

There can be many reasons why soy candle makers would want to sell their candles, such as generating some additional money to buy new supplies or equipment.

The donated items are sold to thrift shops throughout the country generating the much needed revenue for the programs and services.

Blogs are another good way of promoting both a poet's writing and also of generating an income.

It will take a few months for your articles to start generating money, but the results can be well worth your time.

Once gluten is ingested, the body triggers an immune response within the small intestine, generating antibodies to counteract the gluten.

Twenty years ago if someone told you that a film about two gay cowboys on the range would be generating the most Oscar buzz a film has generated since Forrest Gump you'd have thought they'd been to one Village People concert too many.

After generating a trip plan, send it to a portable hand held device or print it to aid during traveling on the open road.

I have more than nine years' experience recruiting and managing a dynamic telesales team at Northco mobile storage, generating company records of $25 million in sales volume each year for the past five years.

Business startup advice includes tips on generating creative business ideas, writing a business plan, finding capital to fund a new business venture, as well as direction for legal, accounting and human resources issues.

Pyramid schemes abound, requiring participants to buy-in so they can recruit others generating profits for those at the top levels generated from new recruits entering at the bottom.

Business proposals allow you to pitch your services to government agencies and private clients, making them an important tool for generating income.

A sprinter, for instance, could improve sprinting speed as the anaerobic system becomes more robust and more effective at generating energy quickly.

Broadcasted by CBS, the show typically attracts up to ten million viewers while generating its fair share of controversy.

Free downloads are great for generating buzz for a band, so you can potentially find them on almost any music-related site.

After Wife Swap began generating buzz around Hollywood, Fox quickly started advertising its own version.

With a name generating tool, it will be easy to find dissimilar names that are still unique and fit your character.

It's a great place to catch up on what people are saying about the most recent movie which is still generating plenty of buzz since its DVD release.

Research is generating breakthroughs in medical technology that rival the magic of Star Trek's bio beds.

The naming team is responsible for generating some of the world's most recognized monikers, and often it is these names that make the colors themselves so memorable.

Find out more about what RSS advertising is and learn how to begin utilizing this technique as a way of generating revenue from your blogging efforts.

EasyPodder - Created for Windows and Linux, this is a one-stop shop for podcast production, generating RSS feeds (as .xml files), ID3 tags, and even providing an FTP tool for uploading your podcast.

Generating a healthy discussion can bring you some nice repeat traffic for your site.

It prompts users on completing an extension request, eventually generating a finished form.

If you aren't planning to create a revenue generating blog, you can host your website on WordPress.com.

Some of these can be specified back in Flash itself before generating the movie, but it is always a good idea to double check your work.

If your Internet search for free forum templates isn't generating sites, you may have better luck by entering one of the other terms.

Invest some time into generating quality content for your site before taking the time to go through submitting your feed to all of the feed directories.

Every page seems to have more and more ads, leading one to suspect that perhaps it is less designed as a showcase and more an ad-revenue generating site.

This allows you the ability to maintain the freedom to customize and modify your website however you wish, while enjoying the traffic generating power that RSS feeds typically offer blogs.

The actual method for generating HTML to represent color is rooted in math and the science of color theory.

Their employees engineer websites to increase a company's profitability by generating sales and targeting prospective customers.

The whole purpose of a site for generating HTML code is to save you the trouble of typing it in yourself.

Some people are aware that most word-processors like Microsoft Word include HTML code generating capabilities.

I could feel tears streaming down my face though I had no recollection of generating them.

Where, however, there are a number of cranes all belonging to the same installation, and these are placed so as to be conveniently worked from a central power station, and where the work is rapid, heavy and continuous, as is the case at large ports, docks and railway or other warehouses, experience has shown that it is best to produce the power in a generating station and distribute it to the cranes.

The apparatus for generating the electric action at one end is commonly called the transmitting apparatus or instrument, or the sending apparatus or instrument, or sometimes simply the transmitter or sender.

These trains are produced by pressing the key in the primary circuit of the induction coil for a longer or shorter time' and generating a long or short series of oscillatory electric sparks between the spark balls with a corresponding creation of trains of electric waves.

Italy has only unimportant lignite and anthracite mines, but water power is abundant and has been largely applied to industry, especially in generating electricity.

Direct reading equidivisional movable coil ammeters can be made in various portable forms, and are very much employed as laboratory instruments and also as ammeters for the measurement of large electric currents in electric generating stations.

In it Maclaurin developed several theorems due to Newton, and introduced the method of generating conics which bears his name, and showed that many curves of the third and fourth degrees can be described by the intersection of two movable angles.

The number of partitions of a biweight pq into exactly i biparts is given (after Euler) by the coefficient of a, z xPy Q in the expansion of the generating function 1 - ax.

Q 1 The Unreduced Generating Function Which Enumerates The Covariants Of Degrees 0, 0' In The Coefficients And Order E In The Variables.

This increase in utility is the same as generating wealth.