where a subscribed element of a matrix is always read as arou, column. Here we confine the element to be real number a vector is a matrix with one row or one column. Therefore a row vector is Alxk and a column vector is AixI and commonly denoted as ak and ai,respec- tively. In the followings of this course, we follow conventional custom to say that a vector is a columnvector except for

The brain is a complex and delicate part of the human organism. It works in special ways through the three systems the Sensory system which functions as receiving information from the outside world; the Motor system which is of the function of sending instructions to the body the Homeostatic system which functions as telling parts of the body how to work or more. But the computer can't do these ways nowadays because it lacks imagination

CHOICE OF LAW IN INTEGRATED AND INTERCONNECTED MARKETS A Matter of Political Economy Horatia Muir Watt laws as an issue of political economy can be seen as a response to the tectonic shiff t of A case of lost innocence: 2 Shifis in the public/private divide. Describing the confl traditional thinking in this field 5 a new generation of collisions of economic regulation o o currently wrought by globalisation in respect of the public/private law divide, which shape

n contrast to alcohols with their rich chemical reactivity, ethers (compounds contain- ing a C-0-C unit) undergo relatively few chemical reactions. As you saw wher we discussed Grignard reagents in Chapter 14 and lithium aluminum hydride reduc- tions in Chapter 15, this lack of reactivity of ethers makes them valuable as solvents in a number of synthetically important transformatio. In the present chapter you will learn

arboxylic acids, compounds of the type RCOH, constitute one of the most fre- quently encountered classes of organic compounds Countless natural products are carboxylic acids or are derived from them. Some carboxylic acids, such as acetic acid, have been known for centuries. Others, such as the prostaglandins, which are pow erful regulators of numerous biological processes remained unknown until relatively

SOLUTIONS TO TEXT PROBLEMS 8.1 Identify the nucleophilic anion in each reactant. The nucleophilic anion replaces bromine as a sub- stituent on carbon. (b) Potassium ethoxide serves as a source of the nucleophilic anion CH,CH,. CH,CH,: CH, Br: CH3CH2OCH3 + Br: Ethoxide ion Methyl bromide Ethyl methyl ether Bromide ion

20.1 () Carboxylic aci id anhydrides bear two acyl groups on oxygen, as in RCOCR. They are named as derivatives of carboxylic acids. Q CH:CH2CHCOH CH,CH,CHCOCCHCH_CH3 C6H C. C. 2-Phenylbutanoic acid 2-Phenylbutanoic anhydride (c) Butyl 2-phenylbutanoate is the butyl ester of 2-phenylbutanoic acid. CH,CH,CHCOCH,CH,CH2CH

Dyspnea is defined as an awareness of difficulty in breathing It is therefore a symptom, usually described by the patient as \shortness of breath,\whether the sensation is due to actual difficulty in breathing or is essentially an awareness of hyperventilation. If the symptom becomes striking, it always companies with dilatation of nares, cyanosis, use of accessory muscles of respiration and abnormalities of respiratory rate, depth or rhythm

Definition: Dyspnea is defined as an awareness of difficulty in breathing It is therefore a symptom, usually described by the patient as \short of breath,\ whether the sensation is due to actual difficulty in breathing or is essentially an awareness of hyperventilation. If the symptom becomes striking, it always companies with dilatation of nares, cyanosis, use of accessory muscles of respiration and abnormalities of respiratory rate, depth or rhythm

Food packaging is a still growing market As a consequence, the demand to re-use post-consumer packaging materials grows as well. Recycling of packaging materials plays an increasing role in packaging, and numerous applications can already be found on the market. Ten or twenty years ago most post-consumer packaging waste was going into landfill sites or to incineration