outside explicit awareness. i shall not attempt to unravel the perplexing mystery of how the cognitive unconscious is acquired and controlled. instead i shall analyze another aspect of unawareness, namely ignorance of features of things and people. examples of this kind of unawareness are perceptual illusions which fool us into overlooking the features of physical objects. we may similarly overlook psychological characteristics of oneself and other people such as motives, emotions, abilities, and attitudes. this ignorance of attributes is what freud ' s concept of the unconscious denoted. in what follows i offer a sociohistorical psychological explanation of this kind of unawareness. sociohistorical psychology explains unawareness of people ' s psychological qualities in terms of the social concepts which structure perception. as discussed earlier, social concepts function as cognitive schemas which structure our mental processes and sensitize us to certain things while desensitizing us to other things. in this way social concepts create unawareness as well as awareness. for example, the social value of romantic love leads to exaggerating the lover ' s attractiveness and obscuring faults. the social value of youthfulness leads to exaggerating the capabilities of young people and obscuring their limits. conversely, the capabilities and wisdom of old people are obscured and denigrated. from this point of view, unawareness and awareness are two sides of the same janus figure. unawareness is the obverse of awareness its dialectical opposite. unawareness is not a separate system as freud claimed. unawareness is due to misperception and it is explainable in the same terms as perceptual illusions : the perceiver invokes incorrect assumptions about a psychological quality and these erroneous assumptions misinform him about its properties, relationships, and origins. asch ( 1952, p. 604 ) explained this as follows : " the forcible exclusion of data ( and goals ) from the center of awareness need not involve the operation of unconscious forces in freud ' s sense. what is of most consequence at the social level is that one does not see facts in their proper context, or that one does not face them, or that one violently stresses certain events at the expense of others, operations which produce misstructuring or distortion in understanding and feeling. " explaining unawareness in the same terms as misperception has several virtues. it sharpens our understanding of unawareness by employing accepted, detailed concepts from the study of " perception and cognition. it also maintains a parsimonious account of


. " explaining unawareness in the same terms as misperception has several virtues. it sharpens our understanding of unawareness by employing accepted, detailed concepts from the study of " perception and cognition. it also maintains a parsimonious account of several phenomena with relatively few concepts, which is one of the goals of science. perception and recollection of psychological characteristics are distorted by inadequate concepts. * distortion occurs in two ways. in certain cases, conceptual schemata lead to misperceiving an enduring quality. for instance, a person of low intelligence believes himself to be bright. his low intelligence persists despite his overestimation. in other cases, conceptual schemata actually transform a psychological quality. for example, an angry person who conceives of herself as mild - mannered may not perceive her own angry state as anger. anger will be misconstrued as equanimity and the latter will be experienced. anger may have been momentarily experienced but it was transformed in the act of reflection and no longer exists. of course, the brief experience of anger may be encoded in memory and remembered as a previous experience. however, in all likelihood, the anger will not be recalled because it was so fleeting and discordant with the individual ' s self image. * * both kinds of misperception leave the subject unaware of the original quality. in neither case does the original quality remain in the subject ' s " unconscious. " low intelligence is not " unconsciously " known to the subject, any more than the real properties of objects are " unconsciously " known in the case of perceptual illusions. social concepts function as filters which distort the character of a psychological quality just as they can distort the properties of physical objects. distortion is caused by conceptual limitations of social values, not, as freudians claim, by the subject ' s fear of facing his or her own unacceptable true ideas. to say that social concepts structure awareness means that all perceptual activity is biased toward certain things and away from others. perception can never be fully responsive to everything. it must be insensitive to, or unaware of, phenomena which fall beyond its parameters. although all social concepts produce some unawareness, the content and extensiveness of unawareness vary. certain concepts may desensitize us to things which are quite valuable, and we will wish to replace these concepts with others that sensitize us to the important things. we shall return to this subject in the section on overcoming unawareness


superficiality, intolerance and insecurity. he could not see that other people were sensitive and justifiably offended by his arrogance. fictitious postulates were necessary to uphold the integrity of his ideological system. george ' s competitive social concept additionally led him to misconstrue the interrelation of certain qualities in himself and others. his competitive schema did not allow him to perceive his awkwardness as a causal factor which pushed people away from him. this would have implied some weakness in george which was inconceivable to his viewpoint. his competitive schema made george reverse the causal relationship and postulate that other people had estranged him, thereby producing his awkwardness. another social concept, atomism, compounded george ' s unawareness. atomism is the belief that phenomena are discrete, independent atoms. atomism, like competition, is rooted in our capitalistic socioeconomic system. the struggle among independent entrepreneurs to maximize their private wealth, unbridled by social coordination, cooperation, or obligation fosters the belief that the world is composed of separate, independent elements ( macpherson, 1962 ). when people regard themselves in these atomistic terms they feel internally fragmented and detached from other people. detachment desensitizes us to other people ' s needs, perceptions, emotions, reasoning, and motives. it also obscures social influences that mold behavior. these effects of atomism can be seen in george ' s psychology. he certainly felt estranged from people, and he was terribly insensitive to their perceptions, emotions, and personality. george ' s atomistic thinking also obscured the interrelationships among his psychological activities. it focused his attention on individual acts and distracted him from detecting consistencies among them. for example, it never occurred to george that shoplifting, spreading rumors, resenting other people ' s success, and lecturing to them all embodied a common tendency to make himself superior. the dissimilar details of these acts overshadowed similar elements. when george succeeded with shoplifting he was absorbed in the success of obtaining a free object. when he lectured people he was absorbed in presenting a clever idea. the different acts each generated a gleeful superiority, but because the acts were not compared together, this feeling was not drawn out as a common essential quality. * * experimental psychologists have reported similar awareness of particular events but unawareness of their relations. kenneth bowers ( 1984 ) described an experiment where he selectively reinforced subjects ' preference for certain pictures. this reinforcement led to dramatic changes in preference for


quality. * * experimental psychologists have reported similar awareness of particular events but unawareness of their relations. kenneth bowers ( 1984 ) described an experiment where he selectively reinforced subjects ' preference for certain pictures. this reinforcement led to dramatic changes in preference for some subjects. these subjects were aware of the reinforcement, but they failed to comprehend the effect that the reinforcement had on their preferences : they insisted that their preferences were independent of the reinforcement. nisbett and wilson ( 1977 ) summarize additional experimental demonstrations of people being aware of factual events but unaware of the causal relation between them. subjects whose behavior has been systematically modified by manipulating certain variables misattribute their behavior to other factors. a final effect that atomistic thinking had on george ' s unawareness was to blind him to the relationship that his behavior had to the broad society. he construed his behavior in individual terms and was oblivious to social factors, including social concepts, which had influenced his action. it is important to understand that social concepts restructured george ' s consciousness to blot out the foregoing characteristics and relationships. george could not entertain these issues because they lay outside his conceptual framework, not because he was afraid to face them. he was unaware of them because they were inconceivable, not because they were unacceptable. knowledge of these issues did not surreptitiously exist in george ' s " unconscious " insulated from social consciousness. rather, competitive and atomistic schemata structured the psyche so thoroughly as to preclude knowledge from existing at any level. the true character and relationships of psychological acts were unknown to george without being unconscious in the freudian sense. according to sociohistorical psychology, unawareness is not the product of negatively blocking an existing idea. it results from positively structuring perception in a certain way that misconstrues qualities and their relationships. unawareness depends upon a certain kind of awareness. for freud, understanding unawareness does not require understanding consciousness. the only aspect of consciousness that is relevant is that it rejects a certain idea as unacceptable. for sociohistorical psychology, understanding unawareness depends upon understanding the specific social concepts of consciousness which value and devalue certain qualities of people, relate and differentiate particular attributes, and which construe events in a certain manner. george ' s conceptual framework not only desensitized him to certain characteristics ( e. g., weaknesses ) and relationships ( e. g., patterns ) of psychological activity. his conceptual framework also obscured the causes of


. social concepts are the means by which we produce psychological phenomena they are our " psychological means of production " and " psychological mode of production. " social concepts not only determine our perceptions, emotions, imagination, and needs, but our unawareness as well. several caveats must be mentioned concerning social ideology and psychology. although ideology is constructed and sustained in social institutions, individuals creatively apply ideology to their particular personal situation. we have seen how hysterical women exaggerated social values to construct psychological symptoms. george was similarly creative in using competition to explain his estrangement. he postulated weaknesses in his peers which led them to reject him. however, he could have utilized the concept of competitiveness to explain his social estrangement in another way. he might have regarded himself as a loser with less ability than his successful peers. blaming oneself for failure is as compatible with competitive ideology as is blaming others. an ideology has numerous strands and the individual may select among them. * the failure of naive individuals to identify the social pattern, significance, and origin of their psychological functions means that a sociohistorical analysis must be made by a culturally sensitive observer rather than by the subject himself. phenomenological reports of subjective experience will not explicate the sociohistorical character of that naive experience. as sartre ( 1960 / 1976, p. 225 ) said, " there is no a priori reason why the... result [ of social events ] should be understood by the agent : everything depends upon the instruments of thought provided for him by his period, class, and historical circumstances. " while a sociohistorical character is implicit in all experience, it can only be explicated by an analyst who is knowledgeable about society and can draw out the manner in which experience reflects ( and contradicts ) social values and norms ( cf. ratner, 1993b ). another caveat is that predominant social values such as competitiveness and atomism do not affect all individuals equally. people have different social experiences and they exercise some selection in adopting social concepts. why a particular individual adopts a particular form of a particular ideology is not addressed here. i am only concerned with the social parameters within which individual variations occur. the social parameters allow for prediction of general psychological trends among masses of people, but not for prediction of any one individual. an individual ' s psychology is composed of social concepts but which particular ones must be discovered after he or she makes the selection. we have seen that unawareness of psychological qualities and relationships is shaped by social


, but not for prediction of any one individual. an individual ' s psychology is composed of social concepts but which particular ones must be discovered after he or she makes the selection. we have seen that unawareness of psychological qualities and relationships is shaped by social influences of which we are also unaware. consequently, overcoming unawareness requires identifying the social influences which produce it, repudiating these influences, and ultimately replacing them with others that enhance sensitivity. the social concepts which generate unawareness can be gleaned from a social analysis of conscious activity. consciousness and unawareness are two sides of the same social concept. the analyst must begin with the social concepts that inform conscious activity and proceed to identify the unawareness which those same concepts produce. for example, george ' s arrogance and stealing were forms of competitiveness, and the latter was responsible for his ignorance about self and others. once conscious activity is construed in social terms, unawareness can be also. reconceptualizing cognitive concepts and behavior in social terms such as competition, materialism, individualism, reification, and alienation restructures understanding because language produces meaning. this meaning - giving function of language was one of vygotsky ' s central concerns. he believed that, " speech does not merely serve as the expression of developed thought. thought is restructured as it is transformed into speech. it is not expressed but completed in the word " ( vygotsky, 1987b, p. 251 ; cf. ratner, 1991, pp. 36 _ 37 ). recasting personal lived experience as reflecting social concepts * provides the greatest potential for identifying, repudiating, and eliminating the causes of personal unawareness. identifying social concepts in the psyche would make george aware of the numerous ways in which he thinks and acts competitively, and how these combine to make him unaware of important issues. * dilthey was an important advocate of this kind of recasting ( cf. - - ermarth, 1978, pp. 226 _ 227 - - ). george would then be in a position to systematically repudiate these psychological manifestations of competition which impair his awareness. identifying social concepts would additionally enable george to identify their origins and manifestations in diverse sectors of society. george could discern that his personal competitiveness was promulgated by competitiveness in the economy, in the media, in school, and elsewhere. he would then be in a position to systematically repudiate the social origins of his destructive behavior and his unawareness


facilitate awareness of the social reasons for his behavior. new social concepts would therefore restructure george ' s psychological field. elements would become reorganized into new relationships, causal vectors would be reversed, and characteristics which appeared immutable might be perceived as changeable. since social concepts emanate from social practice, new beneficent concepts can only be successfully implemented if they are supported by a new social practice, just as debilitating social concepts can only be uprooted if their social basis is repudiated. sociohistorical psychology is unique in emphasizing the social changes necessary to enhance awareness. nonsocial analyses ignore the full range of social and psychological influences which sustain unawareness. nonsocial analyses also pay little attention to reconstructing new social practices and concepts that must replace the debilitating ones. this makes overcoming unawareness extremely difficult because the sustaining context continues to perpetuate it. paradoxically, overlooking social systems reifies behavior as natural, while recognizing social origins and social forms of behavior enable them to be altered. social practices and concepts can be altered for a variety of reasons. one reason is that social practices and concepts may produce behavior that contradicts them. for example, competition is designed to motivate winning behavior, but it often produces losing behavior. people who consistently lose may see the contradiction between what the social value promises and what it actually produces. the social value cannot deliver its own definition of success. this internal contradiction may lead to questioning the viability of the social concept. another reason for altering social concepts is the " external " contradiction that occurs between different concepts. every society has numerous social concepts which reflect activities from different social sectors. in the united states, competition is contradicted by religious, family, and educational values. internal and external contradictions among social concepts can generate psychic strife and the desire to change behavior. there is no need to postulate a non - social segment of self which challenges and improves social concepts. according to sociohistorical psychology, psychological qualities are not unknown because they are submerged below conscious awareness. they are unknown because they lie beyond the scope of our conceptual schemata. psychological insight will not be achieved by a depth psychology which excavates impulses from inside the mind. insight requires breadth psychology which develops new social concepts and social relations. this is what vygotsky ( 1987a, p. 77 ) had in mind when he said, " it is not the depths but the heights of the personality that are decisive for understanding the reactions of


carl e. wieman, wendy k. adams, and katherine k. perkins this item is a 2008 article in science magazine that highlights research done by the physics education technology project on how students use interactive simulations to meet their learning needs. the article discusses research by the phet project on the design and use of simulations in a variety of educational settings. results indicate that concept mastery is measurably improved when students explore simulations in addition to traditional labs. in addition, use of simulations was correlated with higher student motivation and active involvement in the learning process. the phet project provides technology - based resources and information for physics education, most notably, simulations on a wide range of topics. the simulations are developed in conjunction with careful research to enhance their effectiveness as learning tools. metadata instance created february 10, 2009 by caroline hall july 8, 2010 by lyle barbato last update when cataloged : october 31, 2008 this resource is part of a physics front topical unit. topic : wave energy unit title : teaching about waves and wave energy a must - read article from science magazine, this item summarizes the research efforts of the phet project on the use of interactive simulations in the physics classroom. results indicate that concept mastery is measurably improved when students explore simulated physical processes in addition to traditional labs. use of simulations was also correlated to higher student motivation and active involvement in the learning process. c. wieman, w. adams, and k. perkins, phet research : simulations that enhance learning, science 322 ( 5902 ), 682 ( 2008 ), < http : / / phet. colorado. edu / publications / phet _ simulations _ that _ enhance _ learning. pdf >. wieman, c., adams, w., & perkins, k. ( 2008, october 31 ). phet research : simulations that enhance learning. science, 322 ( 5902 ), 682 - 683. retrieved may 23, 2013, from http : / / phet. colorado. edu / publications / phet _ simulations _ that _ enhance _ learning. pdf % 0 journal article % a wieman, carl % a adams, wendy % a perkins, katherine % d october 31, 2008 % t phet research : simulations that enhance learning % j science % v 322 % n 5902 % p 682 - 683 % 8 october 31, 2008 % u http : / / phet. colorado. edu / publications / phet _ simulations _ that _ enhance _ learning. pdf


the item that binds the two hard - to - combine ingredients. common emulsifiers are mustard and egg yolks. glaze : 1. a 90 % reduction of stock. 2. a thin glossy coating applied to foods. a reduction or aspic can cover savory foods. anything from melted chocolate to thin icings can cover pastries and cakes. v. to apply a thin shiny coating to food. infusion : the extraction of flavor from a food in a hot liquid ( below the boiling point ). usually refers to teas and coffees, but can also apply to cooking ( like the pistachio cream or olive oils that are infused with herbs ). infusion : the extraction of flavor from a food in a hot liquid ( below the boiling point ). usually refers to teas and coffees, but can also apply to cooking ( like the pistachio cream or olive oils that are infused with herbs ). - j - marrow : a soft, fatty tissue found in the hollow center of an animal ' s bone - - particularly plentiful in the shin and leg bones. considered a delicacy in europe, marrow is light and digestible with the same amount of calories as beef fat. it can be cooked in the bone, removed, and eaten. and it can be used in soups and stews for flavor and body. mince : to cut food into very small pieces. the terms " finely chopped " and " minced " are interchangeable. mirepoix : [ mihr - pwah ] a mixture of diced carrots, onions, celery, and herbs sauteed in butter. mirepoix is used in almost all soups, sauces, and stews as a base flavor. it is also used as a bed to braise meats, poultry and fish. mount : a technique where small pieces of cold, unsalted butter are whisked into a sauce just before serving. mounting gives sauces texture and flavor as well as a glossy look. non - reactive : any cooking material that won ' t react ( by discoloring or changing the taste ) with acidic foods. glass and stainless steel are the most common non - reactive materials. non - reactive pan or bowl : any non - porous material that does not impart a flavor or alter a color in food. this includes glass, stainless steel, glazed ceramic, or enamel. - p - poach : to cook food gently in hot liquid that


or bowl : any non - porous material that does not impart a flavor or alter a color in food. this includes glass, stainless steel, glazed ceramic, or enamel. - p - poach : to cook food gently in hot liquid that ' s just below the boiling point. liquids can vary from broths, to water, to syrups. polenta : [ po - lehn - tah ] an italian cornmeal mush that is often cooled and then fried, grilled, broiled, or baked. prosciutto : [ proh - shoo - toh ] this " ham " is italy ' s gift to the food world. the cities of parma and san daniele ( where it ' s mainly produced ) argue over whose is better. its production is a secret. it ' s first seasoned and salt - cured ( but not smoked ). then it ' s air - dried, pressed, and sold thinly sliced. the best hams are aged 18 to 24 months. - r - reduce : applied to cooking, this means to boil a liquid until its volume is reduced by evaporation. this thickens the liquid and intensifies the flavor. reduction : a process used to increase and intensify the flavor of a liquid. this is done by rapidly boiling a liquid to decrease its volume through evaporation. this concentrates the flavor, so season a reduction after it ' s made - - not before. render : the melting of animal fat over low heat so it separates from any connective tissue. this tissue turns crisp and brown ( known as crackling ) and the clarified ( clear ) fat is further processed by straining. to cook fatty meats, such as bacon or spare ribs, until the fat melts. resting : heat drives meat ' s juices from the surface when it cooks. letting meat " rest " before slicing lets these juices seep back towards the surface ( liquids always take the path of least resistance ). the result is a more flavorful piece of meat. ribbon : when a sauce thickens enough that when lifted, it falls in wide bands. also, when sauce is thick enough that while stirred with a whisk, it leaves trails that expose the bottom of the pan or mixing bowl. ricer : a kitchen gadget that looks like a big garlic press. great for mashing potatoes. this device, also called a potato ricer, forces cooked foods like turnips saute : [ saw - tay ] in french


net force, also known as resultant force, is a vector quantity produced when two or more forces act upon one object. the concept of net force is the same as the mathematical concept of vector addition. let ' s talk about net force. this is also sometimes called resultant force, those two words are used interchangenly and basically what this is, is the vector that ' s produced when 2 or more forces act together. remember anything that has distance and magnitude we can depict as a vector. so let ' s look at a couple of examples or how you can calculate a net force on an object okay. let ' s take for example a helicopter, you may notice when helicopters go up and down they are completely vertical right? but when they want to go forward they need to actually tilt, that ' s to create this thrust where they ' re pushing air in that direction which is causing a force in that direction. i ' m going to call that f1 okay but how come that a helicopter that ' s tilted in this direction isn ' t going up in that direction? well that ' s because there ' s a second force acting on that helicopter okay and that ' s the force of gravity. i ' m going to call that f2, okay. so what ' s the overall force going to be on this helicopter? well i have to add my 2 vectors together and i can do that easily by just taking this one and pointing it head to tail to the first one. so if i put my f2 right here i can see that my resultant vector which we ' ll call fa is causing it to move in a horizontal way to the earth. okay, so just adding vectors that helps us figure out the true vector okay. let ' s say i ' m playing golf another example we might see i ' m going to tee off from right here and there ' s my hole and i want to aim right for that whole okay and i ' m going to hit a shot that goes right about there okay. now if that was my only force acting on that ball that would be a pretty good shot right. but let ' s say there ' s a wind and let ' s say that wind is blowing in this direction okay. so f1 is the force applied to my golf club on the ball, f2 is the wind okay. that is going to push the ball in this direction, okay so i put f2 right there and i add these two vectors together and i actually get something that looks like that f actual okay and now i ' m


in mathematics, computer science, or management science, mathematical optimization ( alternatively, optimization or mathematical programming ) is the selection of a best element ( with regard to some criteria ) from some set of available alternatives. in the simplest case, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. the generalization of optimization theory and techniques to other formulations comprises a large area of applied mathematics. more generally, optimization includes finding " best available " values of some objective function given a defined domain, including a variety of different types of objective functions and different types of domains. optimization problems an optimization problem can be represented in the following way - given : a function f : a r from some set a to the real numbers - sought : an element x0 in a such that f ( x0 ) ≤ f ( x ) for all x in a ( " minimization " ) or such that f ( x0 ) ≥ f ( x ) for all x in a ( " maximization " ). such a formulation is called an optimization problem or a mathematical programming problem ( a term not directly related to computer programming, but still in use for example in linear programming – see history below ). many real - world and theoretical problems may be modeled in this general framework. problems formulated using this technique in the fields of physics and computer vision may refer to the technique as energy minimization, speaking of the value of the function f as representing the energy of the system being modeled. typically, a is some subset of the euclidean space rn, often specified by a set of constraints, equalities or inequalities that the members of a have to satisfy. the domain a of f is called the search space or the choice set, while the elements of a are called candidate solutions or feasible solutions. the function f is called, variously, an objective function, cost function ( minimization ), indirect utility function ( minimization ), utility function ( maximization ), or, in certain fields, energy function, or energy functional. a feasible solution that minimizes ( or maximizes, if that is the goal ) the objective function is called an optimal solution. by convention, the standard form of an optimization problem is stated in terms of minimization. generally, unless both the objective function and the feasible region are convex in a minimization problem, there may be several local minima, where a local minimum x * is defined as a point


- optimal control theory is a generalization of the calculus of variations. - dynamic programming studies the case in which the optimization strategy is based on splitting the problem into smaller subproblems. the equation that describes the relationship between these subproblems is called the bellman equation. - mathematical programming with equilibrium constraints is where the constraints include variational inequalities or complementarities. multi - objective optimization adding more than one objective to an optimization problem adds complexity. for example, to optimize a structural design, one would want a design that is both light and rigid. because these two objectives conflict, a trade - off exists. there will be one lightest design, one stiffest design, and an infinite number of designs that are some compromise of weight and stiffness. the set of trade - off designs that cannot be improved upon according to one criterion without hurting another criterion is known as the pareto set. the curve created plotting weight against stiffness of the best designs is known as the pareto frontier. a design is judged to be " pareto optimal " ( equivalently, " pareto efficient " or in the pareto set ) if it is not dominated by any other design : if it is worse than another design in some respects and no better in any respect, then it is dominated and is not pareto optimal. the choice among " pareto optimal " solutions to determine the " favorite solution " is delegated to the decision maker. in other words, defining the problem as multiobjective optimization signals that some information is missing : desirable objectives are given but not their detailed combination. in some cases, the missing information can be derived by interactive sessions with the decision maker. multi - objective optimization problems have been generalized further to vector optimization problems where the ( partial ) ordering is no longer given by the pareto ordering. multi - modal optimization optimization problems are often multi - modal ; that is, they possess multiple good solutions. they could all be globally good ( same cost function value ) or there could be a mix of globally good and locally good solutions. obtaining all ( or at least some of ) the multiple solutions is the goal of a multi - modal optimizer. classical optimization techniques due to their iterative approach do not perform satisfactorily when they are used to obtain multiple solutions, since it is not guaranteed that different solutions will be obtained even with different starting points in multiple runs of the algorithm. evolutionary algorithms are however a very popular approach to obtain multiple solutions in a multi -


evaluation of hessians. - gradient descent ( alternatively, " steepest descent " or " steepest ascent " ) : a ( slow ) method of historical and theoretical interest, which has had renewed interest for finding approximate solutions of enormous problems. - subgradient methods - an iterative method for large locally lipschitz functions using generalized gradients. following boris t. polyak, subgradient – projection methods are similar to conjugate – gradient methods. - bundle method of descent : an iterative method for small – medium sized problems with locally lipschitz functions, particularly for convex minimization problems. ( similar to conjugate gradient methods ) - ellipsoid method : an iterative method for small problems with quasiconvex objective functions and of great theoretical interest, particularly in establishing the polynomial time complexity of some combinatorial optimization problems. it has similarities with quasi - newton methods. - reduced gradient method ( frank – wolfe ) for approximate minimization of specially structured problems with linear constraints, especially with traffic networks. for general unconstrained problems, this method reduces to the gradient method, which is regarded as obsolete ( for almost all problems ). - simultaneous perturbation stochastic approximation ( spsa ) method for stochastic optimization ; uses random ( efficient ) gradient approximation. - methods that evaluate only function values : if a problem is continuously differentiable, then gradients can be approximated using finite differences, in which case a gradient - based method can be used. global convergence more generally, if the objective function is not a quadratic function, then many optimization methods use other methods to ensure that some subsequence of iterations converges to an optimal solution. the first and still popular method for ensuring convergence relies on line searches, which optimize a function along one dimension. a second and increasingly popular method for ensuring convergence uses trust regions. both line searches and trust regions are used in modern methods of non - differentiable optimization. usually a global optimizer is much slower than advanced local optimizers ( such as bfgs ), so often an efficient global optimizer can be constructed by starting the local optimizer from different starting points. - memetic algorithm - differential evolution - differential search algorithm matlab code - link has been provided in civicioglu, p., ( 2012 ). - dynamic relaxation - genetic algorithms - hill climbing - nelder - mead simplicial heuristic : a popular heuristic for approximate minimization


- link has been provided in civicioglu, p., ( 2012 ). - dynamic relaxation - genetic algorithms - hill climbing - nelder - mead simplicial heuristic : a popular heuristic for approximate minimization ( without calling gradients ) - particle swarm optimization - artificial bee colony optimization - simulated annealing - tabu search - reactive search optimization ( rso ) implemented in lionsolver mechanics and engineering problems in rigid body dynamics ( in particular articulated rigid body dynamics ) often require mathematical programming techniques, since you can view rigid body dynamics as attempting to solve an ordinary differential equation on a constraint manifold ; the constraints are various nonlinear geometric constraints such as " these two points must always coincide ", " this surface must not penetrate any other ", or " this point must always lie somewhere on this curve ". also, the problem of computing contact forces can be done by solving a linear complementarity problem, which can also be viewed as a qp ( quadratic programming ) problem. many design problems can also be expressed as optimization programs. this application is called design optimization. one subset is the engineering optimization, and another recent and growing subset of this field is multidisciplinary design optimization, which, while useful in many problems, has in particular been applied to aerospace engineering problems. economics is closely enough linked to optimization of agents that an influential definition relatedly describes economics qua science as the " study of human behavior as a relationship between ends and scarce means " with alternative uses. modern optimization theory includes traditional optimization theory but also overlaps with game theory and the study of economic equilibria. the journal of economic literature codes classify mathematical programming, optimization techniques, and related topics under jel : c61 - c63. in microeconomics, the utility maximization problem and its dual problem, the expenditure minimization problem, are economic optimization problems. insofar as they behave consistently, consumers are assumed to maximize their utility, while firms are usually assumed to maximize their profit. also, agents are often modeled as being risk - averse, thereby preferring to avoid risk. asset prices are also modeled using optimization theory, though the underlying mathematics relies on optimizing stochastic processes rather than on static optimization. trade theory also uses optimization to explain trade patterns between nations. the optimization of market portfolios is an example of multi - objective optimization in economics. since the 1970s, economists have modeled dynamic decisions over time using control theory. for example, microeconomists use dynamic


of economic science, macmillan, p. 16. - a. k. dixit ( 1990 ). optimization in economic theory, 2nd ed., oxford. description and contents preview. - a. g. malliaris ( 2008 ). " stochastic optimal control, " the new palgrave dictionary of economics, 2nd edition. abstract. - julio rotemberg and michael woodford ( 1997 ), " an optimization - based econometric framework for the evaluation of monetary policy. nber macroeconomics annual, 12, pp. 297 - 346. - from the new palgrave dictionary of economics ( 2008 ), 2nd edition with abstract links : • " numerical optimization methods in economics " by karl schmedders • " convex programming " by lawrence e. blume • " arrow – debreu model of general equilibrium " by john geanakoplos. further reading undergraduate level - bradley, s. ; hax, a. ; magnanti, t. ( 1977 ). applied mathematical programming. addison wesley. - rardin, ronald l. ( 1997 ). optimization in operations research. prentice hall. p. 919. isbn 0 - 02 - 398415 - 5. unknown parameter - strang, gilbert ( 1986 ). introduction to applied mathematics. wellesley, ma : wellesley - cambridge press ( strang ' s publishing company ). pp. xii + 758. isbn 0 - 9614088 - 0 - 4. mr 870634. graduate level - magnanti, thomas l. ( 1989 ). " twenty years of mathematical programming ". in cornet, bernard ; tulkens, henry. contributions to operations research and economics : the twentieth anniversary of core ( papers from the symposium held in louvain - la - neuve, january 1987 ). cambridge, ma : mit press. pp. 163 – 227. isbn 0 - 262 - 03149 - 3. mr 1104662. - minoux, m. ( 1986 ). mathematical programming : theory and algorithms ( translated by steven vajda from the ( 1983 paris : dunod ) french ed. ). chichester : a wiley - interscience publication. john wiley & sons, ltd. pp. xxviii + 489. isbn 0 - 471 - 90170 - 9. mr 2571910. ( 2008 second ed., in french : programmation mathematique : theorie et algorithmes. editions tec & doc, paris, 2008


489. isbn 0 - 471 - 90170 - 9. mr 2571910. ( 2008 second ed., in french : programmation mathematique : theorie et algorithmes. editions tec & doc, paris, 2008. xxx + 711 pp. isbn 978 - 2 - 7430 - 1000 - 3. unknown parameter - nemhauser, g. l. ; rinnooy kan, a. h. g. ; todd, m. j., eds. ( 1989 ). optimization. handbooks in operations research and management science 1. amsterdam : north - holland publishing co. pp. xiv + 709. isbn 0 - 444 - 87284 - 1. mr 1105099. - j. e. dennis, jr. and robert b. schnabel, a view of unconstrained optimization ( pp. 1 – 72 ) ; - donald goldfarb and michael j. todd, linear programming ( pp. 73 – 170 ) ; - philip e. gill, walter murray, michael a. saunders, and margaret h. wright, constrained nonlinear programming ( pp. 171 – 210 ) ; - ravindra k. ahuja, thomas l. magnanti, and james b. orlin, network flows ( pp. 211 – 369 ) ; - w. r. pulleyblank, polyhedral combinatorics ( pp. 371 – 446 ) ; - george l. nemhauser and laurence a. wolsey, integer programming ( pp. 447 – 527 ) ; - claude lemarechal, nondifferentiable optimization ( pp. 529 – 572 ) ; - roger j - b wets, stochastic programming ( pp. 573 – 629 ) ; - a. h. g. rinnooy kan and g. t. timmer, global optimization ( pp. 631 – 662 ) ; - p. l. yu, multiple criteria decision making : five basic concepts ( pp. 663 – 699 ). - shapiro, jeremy f. ( 1979 ). mathematical programming : structures and algorithms. new york : wiley - interscience [ john wiley & sons ]. pp. xvi + 388. isbn 0 - 471 - 77886 - 9. mr 544669. - spall, j. c. ( 2003 ), introduction to stochastic search and optimization : estimation, simulation, and control,


+ 388. isbn 0 - 471 - 77886 - 9. mr 544669. - spall, j. c. ( 2003 ), introduction to stochastic search and optimization : estimation, simulation, and control, wiley, hoboken, nj. continuous optimization - mordecai avriel ( 2003 ). nonlinear programming : analysis and methods. dover publishing. isbn 0 - 486 - 43227 - 0. - bonnans, j. frederic ; gilbert, j. charles ; lemarechal, claude ; sagastizabal, claudia a. ( 2006 ). numerical optimization : theoretical and practical aspects. universitext ( second revised ed. of translation of 1997 french ed. ). berlin : springer - verlag. pp. xiv + 490. doi : 10. 1007 / 978 - 3 - 540 - 35447 - 5. isbn 3 - 540 - 35445 - x. mr 2265882. - bonnans, j. frederic ; shapiro, alexander ( 2000 ). perturbation analysis of optimization problems. springer series in operations research. new york : springer - verlag. pp. xviii + 601. isbn 0 - 387 - 98705 - 3. mr 1756264. - boyd, stephen p. ; vandenberghe, lieven ( 2004 ). convex optimization ( pdf ). cambridge university press. isbn 978 - 0 - 521 - 83378 - 3. retrieved october 15, 2011. - jorge nocedal and stephen j. wright ( 2006 ). numerical optimization. springer. isbn 0 - 387 - 30303 - 0. - ruszczynski, andrzej ( 2006 ). nonlinear optimization. princeton, nj : princeton university press. pp. xii + 454. isbn 978 - 0691119151. mr 2199043. combinatorial optimization - r. k. ahuja, thomas l. magnanti, and james b. orlin ( 1993 ). network flows : theory, algorithms, and applications. prentice - hall, inc. isbn 0 - 13 - 617549 - x. - william j. cook, william h. cunningham, william r. pulleyblank, alexander schrijver ; combinatorial optimization ; john wiley & sons ; 1 edition ( november 12, 1997 ) ; isbn 0 - 471 - 55894 - x. - gondran, michel ; minoux, michel ( 1984 ). graphs and algorithms


| s - block in the periodic table | | | this article is in a list format that may be better presented using prose. ( march 2013 ) | the s - block is a block in the periodic table that consists of the first two groups, namely the alkali metals and the alkaline earth metals. the elements in the s - block generally exhibit well - defined trends in their physical and chemical properties, changing steadily moving down the groups. their properties can be most readily explained in terms of their electron configuration, with their valence electrons occupying s - orbitals. by this definition, hydrogen and helium are sometimes also considered to be part of the s - block. the modern periodic law states that an element ' s chemical and physical properties is a periodic function of its atomic number. the long form of the periodic table is based on modern periodic law. the long form is divided into four blocks, s, p, d, and f. in an atom of an s - block element, the last electron enters the s - orbital of the outermost electron shell : - group 1 : - group 2 : - beryllium ( z = 4 ), magnesium ( z = 12 ), calcium ( z = 20 ), strontium ( z = 38 ), barium ( z = 56 ), radium ( z = 88 ). - anomalous properties of lithium : diagonal relationship | | this section may stray from the topic of the article into the topic of another article, diagonal relationship. ( march 2013 ) | 1. ) lithium is in group 1 and period 2. 2 ) magnesium is in 2 group and 3 period. 3. ) lithium resembles magnesium which is diagonally placed. ¤ cause of diagonal relationship - lithium and magnesium have similar ionic size and polarizing power hence they show diagonal relationship. ¤ similarities between lithium and magnesium - due to similar ionic size and polarizing power. ' li ' and ' mg ' shows similar properties. 1 ) both li and mg are hard metals. 2 ) licl and mgcl2 are deliquecent and crystallize as hydrates. licl. 2h2o and mgcl. 2h2o. 3 ) both li and mg combine with nitrogen to form nitrides. 4 ) hydroxides of both li and mg are weak bases. 5 ) carbonates of both li and mg decompose on heating. 6 ) hydrogen carbonates of both li and mg do not exist in solid states. anomalous behaviour of lithium lithium - the first


both li and mg are weak bases. 5 ) carbonates of both li and mg decompose on heating. 6 ) hydrogen carbonates of both li and mg do not exist in solid states. anomalous behaviour of lithium lithium - the first element of group 1 - differs from the rest of this group in many respects. this anomalous behaviour of lithium is due to the following reasons : - small size of lithium atom and its ion. - higher polarization power of li + ( i. e. charge size ratio ) resulting in increased covalent character of its compounds which is responsible for their solubility in organic solvents - comparatively high ionisation enthalpy and low electropositive character of lithium as compared to other alkali metals - strong intermetallic bonding some of the properties in which lithium differs from other members of its group illustrating its anomalous behaviour are as follows : - lithium is harder than sodium and potassium which are so soft that they can be cut by a knife. - the melting and boiling points of lithium are comparatively high. - lithium forms monoxide with oxygen, other alkali form peroxide and superoxide. - lithium combines with nitrogen to form nitrides, while other alkali metals do not. - lithium chloride is deliquescent and crystallizes as a hydrate licl. 2h2o, whereas other alkali metal chlorides do not form hydrates. - hydroxide of alkali metals don ' t decompose but lioh decompose in li2o + h2o - lithium carbonate decompose on heating into li2o + co2 but rest of all decompose as moh + h2o + co2 - alkali nitrate make nitrites and o2 on heating but li2no3 decompose into li2o and gives brown colour gas no2 and o2 see also


as we work with coalgebras, we ’ ll need a nice way to write out the comultiplication of an element. in the group algebra we ’ ve been using as an example, we just have, but not all elements are so cleanly sent to two copies of themselves. and other comltiplications in other coalgebras aren ’ t even defined so nicely on any basis. so we introduce the so - called “ sweedler notation ”. if you didn ’ t like the summation convention, you ’ re going to hate this. okay, first of all, we know that the comultiplication of an element is an element of the tensor square. thus it can be written as a finite sum now, this uses two whole new letters, and, which might be really awkward to come up with in practice. instead, let ’ s call them and, to denote the first and second factors of the comultiplication. we ’ ll also move the indices to superscripts, just to get them out of the way. the whole index - summing thing is a bit awkward, especially because the number of summands is different for each coalgebra element. let ’ s just say we ’ re adding up all the terms we need to for a given : then if we ’ re really pressed for space we can just write. since we don ’ t use a subscript in parentheses for anything else, we remember that this is implicitly a summation. let ’ s check out the counit laws in this notation. now they read. or, more expansively : similarly, the coassociativity condition now reads in the sweedler notation we ’ ll write both of these equal sums as or more simply as. as a bit more practice, let ’ s write out the condition that a linear map between coalgebras is a coalgebra morphism. the answer is that must satisfy notice here that there are implied summations here. we are not asserting that all the summands are equal, and definitely not that ( for instance ). sweedler notation hides a lot more than the summation convention ever did, but it ’ s still possible to expand it back out to a proper summation - heavy format when we need to.


key : " s : " = show synset ( semantic ) relations, " w : " = show word ( lexical ) relations display options for sense : ( gloss ) " an example sentence " - s : ( n ) chewing gum, gum ( a preparation ( usually made of sweetened chicle ) for chewing ) - s : ( n ) gingiva, gum ( the tissue ( covered by mucous membrane ) of the jaws that surrounds the bases of the teeth ) - s : ( n ) gum ( any of various substances ( soluble in water ) that exude from certain plants ; they are gelatinous when moist but harden on drying ) - s : ( n ) glue, gum, mucilage ( cement consisting of a sticky substance that is used as an adhesive ) - s : ( n ) gumwood, gum ( wood or lumber from any of various gum trees especially the sweet gum ) - s : ( n ) gum tree, gum ( any of various trees of the genera eucalyptus or liquidambar or nyssa that are sources of gum ) - s : ( v ) gum ( cover, fill, fix or smear with or as if with gum ) " if you gum the tape it is stronger " - s : ( v ) mumble, gum ( grind with the gums ; chew without teeth and with great difficulty ) " the old man had no teeth left and mumbled his food " - s : ( v ) gum ( become sticky ) - s : ( v ) gum ( exude or form gum ) " these trees gum in the spring "


this is the second dimension of color and is possibly the simplest to understand. it is, according to albert munsell ' s definition, " the quality by which we distinguish a light color from a dark one. " we noted that the first dimension did not tell us whether a color was light or dark. it told us that the color was green and not red, but we know that there may be light green and dark green. the function of value is to tell us how light or how dark a given color is. for this purpose we shall need a scale of value, which we may conceive as a vertical pole, or axis, to our circle of hues. black is at the lower end, representing total absence of light. white is at the top, representing pure light. between these are a number of divisions of gray, regularly graded between black and white. this gradation could also be infinite. since pure black is unattainable, we will call that 0 and begin our scale with the darkest gray as 1, numbering the steps up to 9, which is the lightest gray. pure white, which is also unattainable, we will call 10. in the practical use of the scale of value, therefore, we shall have but 9 steps and the middle one of these will be 5 - what is referred to as middle value. these steps of value, have been scientifically measured and registered by means of an instrument called a photometer. * in writing a color formula we express this dimension of value by a numeral, which denotes at what step upon the scale of value this color falls. this numeral is written above a line, as b 6 / for example, by which we mean that this particular blue, regardless of its other qualities, is as light or as dark as the 6th step upon the scale of value. a color such as is commonly called " maroon " is an example of a red which is low in value, because it is dark. what is called " pink " is a red which is high in value because it is light. now having familiarized ourselves with these two dimensions and understanding what qualities of a color they express, we may proceed to consider the third dimension. without this third dimension our description of any given color is incomplete. * this instrument is described in albert munsell ' s book, " a color notation. " munsell color co., boston, 1919, p. 38.


the original question was : … true randomness on a quantum level has experimentally been shown to exist. my question is, does this quantum randomness ever / often / always bubble up to our readily observable world of newtonian physics to create truly random everyday events? physicist : hard to say. quick aside : the difference between quantum randomness, which is absolute, and classical randomness, which basically means “ very hard to predict ”, is covered a bit in this older post. in a nutshell, up until the science of quantum mechanics came along it was assumed that if you ( somehow ) knew everything about an object at one moment, you would be able to perfectly predict how it behaved the next. however, it turns out that even if you know absolutely everything about a radioactive atom, for example, it ’ s still impossible to accurately predict when it will decay. this is called “ fundamental ”, “ irreducible ”, or “ quantum ” randomness. back to the point : large scale effects can be thought of in terms of lots of small - scale effects being averaged together which usually ( and counter - intuitively ) leads to much more predictable ( classical ) results. this is the same idea that shows up when you flip lots of coins : the total number of heads is very predictably about half. generally speaking, any individual quantum event will be drowned out by the noise of all of the other quantum events around it, and the average is the only important thing. large scale events that rely on a small number of atoms and interactions are likely to have the same kind of randomness as “ legit ” quantum phenomena. for example, the meter on a geiger counter is an example of quantum randomness on a large - scale. nuclear decay is a quantum mechanically random process. normally, the effects of nuclear decay are washed out. for example, you ’ re hit, on average, by about one high energy particle per exposed square centimeter every second. ever notice? but a geiger counter detects every high energy particle that passes through its detector ( the wand on the right ) and notes the event by moving a needle ( which is huge by quantum standards ) and clicking. so, what geiger counters and other sensitive detectors do is “ exaggerate ” tiny events and bring their effects into the macro - scale. normally, large - scale events are fairly well determined. whether or not you go to lunch is probably not particularly random. if someone somehow got every possible piece of information about what everything in the nearby


events and bring their effects into the macro - scale. normally, large - scale events are fairly well determined. whether or not you go to lunch is probably not particularly random. if someone somehow got every possible piece of information about what everything in the nearby universe was doing, they ’ d be able to predict large - scale events, including your lunch schedule, with fair accuracy. however, if you determine whether or not to go to lunch based entirely on the results of a geiger counter reading, then your lunch outing is a genuine, fundamentally random event. this wouldn ’ t change the experience ; you won ’ t see different versions of yourself walking around, and you won ’ t end up “ spread thin ” across different versions of the universe. a quantum random number generator is essentially the same as an ordinary random number generator. that all said, there ’ s chaos inherent to most of the stuff that happens in the world ( tiny errors becoming bigger errors, becoming bigger errors, … ). however, there ’ s nothing particularly special about the original source of the errors being quantum mechanical. as far as prediction goes, randomness due to quantum mechanics and randomness due to a lack of perfect knowledge ( which is pretty hard to avoid ) are pretty much the same. this is a pretty subtle distinction. you can expect that, after a lot of time, the randomness of quantum processes will lead to worlds that are wildly different from each other because of the butterfly effect. but that ’ s pretty unsatisfying. it would be more interesting to be able to point at a large thing in the world and say “ that is dependent on just a couple of quantum events ”. the most dramatic example of exactly that is probably biological life. the earliest development of a creature is strongly influenced by the interactions of a relatively small number of chemical interactions. an atom in the wrong place in the flagella motor of a sperm can determine whether or not someone is born at all. more than that, the evolution of entire species can be changed by a single mistake in the replication of a strand of dna ( this is one mechanism for mutation ). on a more individual basis, it ’ s hard to say how much the process of thinking is affected by the actions of just a few atoms. the fact that you can lose a heck of a lot of brain cells without noticing implies that the activity of a handful of atoms probably isn ’ t too important when it comes to human behavior. that said ; maybe? by the way, it ’ s a little dangerous to tread this


jumping droplets key to energy efficient products microscopic water droplets jumping from one surface to another could hold the key to a wide array of more energy efficient products — from large solar panels to compact laptop computers, say scientists. a team at duke university has, in fact, developed a new way of producing thermal diodes, devices which regulate heat to preferentially flow in a certain direction, effectively creating a thermal conductor in the forward direction and an insulator in the reverse direction. while thermal diodes can be made from solid materials, these solid - state diodes are not nearly as effective as “ phase - change ” thermal diodes that rely on vaporisation and condensation to transport heat, say the scientists. these phase - change diodes can transfer over a hundred times more heat in the forward direction compared to the reverse, but with major limitations — they are dependent on gravity or restricted by a tubular configuration. these limitations severely constrain the application of phase - change thermal diodes, for example, in mobile electronics which require orientation independence or solar panels which require a large surface area. the duke engineers believe they have figured out a way to solve these limitations to existing thermal diodes by exploiting self - propelled water droplets, which can jump from a superhydrophobic ( highly water - repellent ) surface to a superhydrophilic ( highly absorbent ) surface, but not the other way around.


included here are more in depth explanations of some of the terms and processes in the nuclear fuel cycle. nuclear fuel is produced utilizing various elements and compounds in reactions that yied the product desired at the various stages. initially uranium is the prime constituent looked for in its natural setting during the exploration phase. the ore body, the rock, that holds the uranium also contains many other elements and compounds. while these remain undisturbed, very little of these components enter the surrounding environment. but once mining is initiated, all of the components are moved throughout the environment and left, in many cases, to contaminate the ground and water systems. while most of the uranium is taken from the mine location, almost all of the other components are left in piles of waste rock and tailings either at the mine or at the mill. below are the various components found in uranium ore bodies. full descriptions can be found on wikepedia. uranium - ( pronounced / jʊˈreɪniəm / ) is a silvery - gray metallic chemical element in the actinide series of the periodic table that has the symbol u and atomic number 92. it has 92 protons and 92 electrons, 6 of them valence electrons. it can have between 141 and 146 neutrons, with 146 ( u - 238 ) and 143 in its most common isotopes. uranium has the highest atomic weight of the naturally occurring elements. uranium is approximately 70 % denser than lead, but not as dense as gold or tungsten. it is weakly radioactive. it occurs naturally in low concentrations ( a few parts per million ) in soil, rock and water, and is commercially extracted from uranium - bearing minerals such as uraninite ( see uranium mining ). a person can be exposed to uranium ( or its radioactive daughters such as radon ) by inhaling dust in air, or by ingesting contaminated water and food. absorbed uranium tends to bioaccumulate and stay for many years in bone tissue because of uranium ' s affinity for phosphates. normal functioning of the kidney, brain, liver, heart, and numerous other systems can be affected by uranium exposure, because in addition to being weakly radioactive, uranium is a toxic metal. uranium is also a reproductive toxicant. in nature, uranium atoms exist as uranium - 238 ( 99. 284 % ), uranium - 235 ( 0. 711 % ), and a very small amount of uranium - 234 ( 0. 0058 % ). uranium decays slowly by emitting an alpha particle. the half


be one of the heavy metals. lead has a bluish - white color when freshly cut, but tarnishes to a dull grayish color when exposed to air. it has a shiny chrome - silver luster when melted into a liquid. lead has the highest atomic number of all stable elements, although the next element, bismuth, has a half - life so long ( longer than the estimated age of the universe ) it can be considered stable. like mercury, another heavy metal, lead is a potent neurotoxin that accumulates in soft tissues and bone over time. lead is a poisonous metal that can damage nervous connections ( especially in young children ) and cause blood and brain disorders. to read a more in depth description please visit the wikipedia link : lead molybdenum - ( pronounced / məˈlɪbdənəm /, from the greek word for the metal " lead " ), is a group 6 chemical element with the symbol mo and atomic number 42. it has the eighth - highest melting point of any element. it readily forms hard, stable carbides, and for this reason it is often used in high - strength steel alloys. molybdenum is found in trace amounts in plants and animals, although excess molybdenum can be toxic in some animals. the ability of molybdenum to withstand extreme temperatures without significantly expanding or softening makes it useful in applications that involve intense heat, including the manufacture of aircraft parts, electrical contacts, industrial motors, and filaments. molybdenum dusts and fumes, as can be generated by mining or metalworking, can be toxic, especially if ingested ( including dust trapped in the sinuses and later swallowed ). low levels of prolonged exposure can cause irritation to the eyes and skin. the direct inhalation or ingestion of molybdenum and its oxides should also be avoided. chronic exposure to 60 to 600 mg mo / m³ can cause symptoms including fatigue, headaches, and joint pains. to read a more in depth description please visit the wikipedia link : molybdenum vanadium - ( ipa : / vəˈneɪdiəm / ) is the chemical element with the symbol v and atomic number 23. it is a soft, ductile, silver - grey metal. most vanadium is used as ferrovanadium as an additive to improve steels. all vanadium compounds should be considered to be toxic.


v and atomic number 23. it is a soft, ductile, silver - grey metal. most vanadium is used as ferrovanadium as an additive to improve steels. all vanadium compounds should be considered to be toxic. the occupational safety and health administration ( osha ) has set an exposure limit of 0. 05 mg / m3 for vanadium pentoxide dust and 0. 1 mg / m3 for vanadium pentoxide fumes in workplace air for an 8 - hour workday, 40 - hour work week. the national institute for occupational safety and health ( niosh ) has recommended that 35 mg / m3 of vanadium be considered immediately dangerous to life and health. this is the exposure level of a chemical that is likely to cause permanent health problems or death. to read a more in depth description please visit the wikipedia link : vanadium in nuclear science, the decay chain refers to the radioactive decay of different discrete radioactive decay products as a chained series of transformations. most radioactive elements do not decay directly to a stable state, but rather undergo a series of decays until eventually a stable isotope is reached. decay stages are referred to by their relationship to previous or subsequent stages. a parent isotope is one that undergoes decay to form a daughter isotope. the daughter isotope may be stable or it may decay to form a daughter isotope of its own. the daughter of a daughter isotope is sometimes called a granddaughter isotope. the four most common modes of radioactive decay are : alpha decay, beta minus decay, beta plus decay ( considered as both positron emission and electron capture ), and isomeric transition. of these decay processes, alpha decay changes the atomic mass number ( a ) of the nucleus, and always decreases it by four. because of this, almost any decay will result in a nucleus whose atomic mass number has the same residue mod 4, dividing all nuclides into four classes. the members of any possible decay chain must be drawn entirely from one of these classes. all four chains also produce helium, from alpha particles. three main decay chains ( or families ) are observed in nature, commonly called the thorium series, the radium series ( not uranium series ), and the actinium series, representing three of these four classes, and ending in three different, stable isotopes of lead. the mass number of every isotope in these chains can be represented as a = 4n, a = 4n + 2, and a = 4n + 3, respectively. the long - lived starting


everyone in the electrical industry, including the electrical apprentice, the journeyman, the master electrician, electrical contractor, electrical engineer, designer, the electrical inspector, et al., seem to use the phrase “ neutral conductor. ” however, until the 2008 national electrical code ( nec ), we did not actually have a definition of a neutral. in the process of determining the definition of a neutral for the 2008 nec, the nec technical committee task group on the definition of “ neutral conductor ” realized two definitions were required to adequately define this seemingly elusive component of the electrical system. the definition of a neutral conductor, as developed by the task group, was derived from the international electrotechnical commission definition of neutral conductor with some minor text changes to adapt to the nec style. this definition read, “ neutral conductor — the conductor connected to the neutral point of a system that is intended to carry current under normal conditions. ” the definition establishes that any conductor connected to a neutral point of an electrical system is intended to carry current under normal conditions. any electricians who find themselves connected to a neutral conductor carrying the imbalanced current of the circuit will certainly verify that the neutral is a current - carrying conductor. most electricians, myself included, also will admit that it is very difficult to “ get off ” the neutral conductor once connected to it since the current is on the load side of the circuit. most people either fall away, breaking the connection if on ground or floor level, or fall off the ladder when not working at grade level. we all count ourselves very lucky to have survived the neutral “ connection. ” whenever possible, work on the circuit in an electrically safe work condition. in other words, ensure the circuit has been locked off, and verify that the circuit is de - energized. upon analyzing the newly developed definition of a “ neutral, ” the task group then decided that a second definition was necessary to further explain the “ neutral point. ” the definition of neutral point was found in the ieee standard c57. 12. 80 - 2002 and read, “ the common point on a wye - connection in a polyphase system or midpoint on a single - phase, 3 - wire system, or midpoint of a single - phase portion of a 3 - phase delta system, or a midpoint of a 3 - wire, direct - current system. ” again, with some minor text changes to fit the nec format, this text was adopted into the 2008 nec. to make the two definitions as technically correct as possible, a