Constants and variables

There are two major classes of data entities in the language - constants and variables. Constants can be decimal, binary (prefixed by and Ob ), and hexadecimal (prefixed by Ox ). Negative constants are represented using two s 

A boolean variable represents one or more signals. Each bit of a Boolean variable corresponds to a signal that can have value 0 or 1. The total number of bits is the size of the variable. If the size is one, then it is a scalar, otherwise, it is a vector. An integer value is rqiresented bit-wise using 2 s complement convention therefore, the acceptable values for a vector of size n range firom —2 /. .. (2 / — 1). The indices of a vector start from 0 to n — 1, where index 0 represents the least significant bit (LSB), and index n — 1 represents the most significant bit (MSB). 

A boolean variable is initialized to z. Furthermore, the value assumed by the variable defined in a given model will not be retained the next time the model is invoked (for process models, the value is not retained when the process restarts). Depending on the decisions of the synthesis system, a boolean variable may be synthesized either as a wire or as a register in the final implementation. 

Static variables are similar to boolean variables, with the semantic difference that their values are retained across procedural invocations. Since static variables have state information, they are always implemented as registers in the resulting hardware. Static variables may be optionally initialized to a pre-specified value upon system reset. The registers implementing static variables can be explicitly loaded by using the load assignment statement. For example. 

If-then-else if cond) stmtl else stmt2 

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IgG antibody molecules are composed of two light chains and two heavy chains joined together by disulfide bonds. Each light chain has one variable domain and one constant domain, while each heavy chain has one variable and three constant domains. All of the domains have a similar three-dimensional structure known as the immunoglobulin fold. The Fc stem of the molecule is formed by constant domains from each of the heavy chains, while two Fab arms are formed by constant and variable domains from both heavy and light chains. The hinge region between the stem and the arms is flexible and allows the arms to move relative to each other and to the stem. 

Harbour, R.J., Fatemi, A., and Mars, W.V., Fatigue crack growth of filled rubber under constant and variable amplitude loading conditions. Fat Fract. Eng. Mat. Struct, 30, 640, 2007. 

The elements of Marx s numerical example are also represented in algebraic terms (Table 2.4b). Consider inputs of constant and variable capital to Department 2. The 1,500 units of constant capital are represented by P anXi, the money output of Department 1 required by Department 2. And the 750 units of variable capital are represented by p2h2l2X2, the amount of consumption goods set aside by Department 2 for its own use. 

Marx uses throughout most of his work, that accumulation of capital entails increases in both the value of the means of production used in production processes and in the value of expenditure on labour power, i.e. increases in both constant and variable capital (original emphasis). 

Following the approach worked out in Chapter 3, Table 4.1 shows that in the Kalecki-type formulation profits in each sector are defined in gross terms, consisting of expenditure on the replacement of existing constant capital and its expansion (C, + e/C.) whereas in Table 4.2 profits (/() are defined in net terms (dC, + dV,). The latter definition of profits is consistent with Marx s interpretation, with the total increment of capital identical to the volume of surplus value, after accounting for the replacement of current inputs of constant and variable capital. 

As discussed earlier, in relation to the single swap approach, it may also be posited that capitalists advance the amount M —M required to purchase the total increment of capital. In addition to funding the production of this capital increment, the monetary advance allows the realization of the volume of surplus value required for its production. Capitalists earn a net volume of profits (surplus value) that is driven by increments dC = dC, + dC2 and dV =dV, + dV2 of constant and variable capital respectively. Ignoring for simplicity the role of capitalist consumption, the total volume of surplus value P = dV + dC is driven by capitalist requirements for new constant and variable capital. 

The starting point for the circulation of money, under the auspices of the Kalecki principle, is the expenditure outlays of the capitalist class. In Table 4.5, the composition of these expenditures is made up of money outlays on capitalist consumption ( ) and new constant and variable capital (dC and dV). Outlays are made by capitalists in each department of production. For example, the capitalists in Department 1 spend 400 units on new constant capital, 100 units on new variable capital and 500 units on capitalist consumption. The outlays on the products of both departments are collected in the final row as total outlays, which sum to 1,750. Depending upon what is purchased, each outlay is also a receipt. Department 1 s purchase of 100 consumer goods from Department 2, for example, is a receipt for Department 2. The final column of Table 4.5 collects these receipts, which make up 1,750. The capitalist class outlays 1,750 in total, which returns to it as 1,750 in receipts. 

However, under expanded reproduction a much more demanding requirement is placed on the circuit of money. Capitalists increase then-capital outlay on new elements of constant and variable capital. If we define dC as new constant capital and dV as new variable capital, there is an extra amount of money (dC + dV) that is required to service expanded... 

In (5.5) borrowing is used to finance all money capital outlays on capitalist consumption (u) and new constant and variable capital (dC + dV) in (5.6) this outlay has a multiplier effect (in proportion m) on total sales. As a consequence, the money circuit is viable without the requirement of a money hoard, accumulated from the previous period s sales. 

Key to this economy s capacity to expand is the production of sufficient surplus value to invest in additional units of capital. Marx assumes that a half of surplus value in Department 1 is invested in this way. For year 1 this means that 500 of the total 1,000 units of surplus value produced in Department 1 are directed to 400 units of new constant capital and 100 units of new variable capital. In year 2 constant capital expands from 4,000 to 4,400 units, and variable capital from 1,000 to 1,100 units, maintaining the 4 1 ratio between constant and variable capital. A new position of balance is established by also maintaining Department 2 at its original 2 1 ratio. 

These macroeconomic questions are posed for a model under which proportionality between Departments 1 and 2 is assumed. Consider again (5.10), which exposes the contradiction in the Domar model between absolute amounts of investment, which create new capacity and changes in investment that drive the required amount of aggregate demand. There you see that investment (/) is made up of increments in constant and variable capital, new goods produced by both departments of production. Similarly, the share of surplus value (e) is derived from the value of labour power, which measures the value of inputs (produced in both departments) congealed in worker consumption goods. These macroeconomic terms aggregate across the two departments they transcend the more micro question of proportionality between the two departments. 

Key to the Bauer model is an assumption that constant capital increases at a higher rate than variable capital - the former increases at 10 per cent per annum and the latter at 5 per cent (ibid. 67). The result is a continual increase in the organic composition of capital, the ratio of constant to variable capital. The rate of surplus value, the ratio of total surplus value to variable capital, is assumed to remain constant at all times. With variable capital increasing at 5 per cent each year, the same increase in the pool of total surplus value takes place, out of which additional increments of constant and variable capital are funded. Capitalist consumption is treated... 

This reduction in the proportion of profits consumed has important consequences for the economy as the simulation is repeated over subsequent periods. Although Bauer was able to demonstrate that expanded reproduction is sustainable over a four-year period Grossmann showed that if the simulation is continued for 35 years then this results in economic breakdown. Table 7.1 shows a steady fall in the proportion of profits consumed until, in year 34, only 2.16 per cent are consumed. The stringent demands of capital accumulation are fulfilled with constant and variable capital increasing by 10 and 5 per cent respectively throughout the 35-year period. The problem, however, is that with variable capital failing to keep pace with constant capital the pool of surplus value extracted from variable capital also fails to keep pace. 

The Bauer/Grossmann interpretation of Marx s reproduction schema can be contrasted with our alternative perspective in which the role of money provides the focus of analysis. For Kalecki (1991c 241), it is capitalist investment and consumption decisions which determine profits, and not vice versa . In the Grossmann approach, however, capitalist consumption is a residual left over once capitalists have decided their production of surplus value, out of which new constant and variable capital are allocated. The capitalist consumption portion of surplus value is not determined by the amount of money advanced at the start of the production period, but by the portion left once production has been completed. 

Using the formula C, + Vt + S], values can be calculated for each department. In Department 1, for example, the total value of output is 120 in Department 2, the total value is 60. In our previous analysis of Marx s reproduction schema, based on the second volume of Capital, it was assumed that these values are also the total prices of each department. However, in the third volume Marx focuses on the organic composition of capital, which measures the ratio (Ct/Vt) between constant and variable capital.2 These ratios vary between 4 and 0.4 in this example. And it is this variation that leads Marx to argue that values cannot be sustained as indicators of price for each department of production. The problem is that the rate of profit (.SVC, + V) for each department is calculated as a ratio between total surplus value and total capital. Yet, for each department its own mass of surplus value is calculated from the variable capital employed. 

Second, this rate of profit is applied to each department s costs of production to establish the amount of profit made. In Department 1, for example, profits of 33.3 are made on the total (constant and variable capital) cost price of 100. The price of production for each sector consists of the cost price plus profits in Department 1 this is 133.3. For this numerical example, prices deviate above value for departments with a high organic composition of capital (+13.3 for Department 1) and below for a low organic composition ( —13.3 for Department 2). Department 3 in the example is neutral, having an average composition of capital. 

Although it is traditional in Marxian frameworks for capitalists to initiate the circulation of money with an advance of constant and variable capital, our previous discussion, in Chapter 4, showed that there are a number of ways in which the circulation of money can be modelled. In the single swap approach all of income is advanced in the Franco-Italian circuit approach only the wage bill is advanced in Nell s mutual exchange approach only wages in the capital goods sector are advanced. Our contribution has been to suggest, under the Kalecki principle (first introduced in Chapter 3), that capitalists advance an amount of money sufficient to realize their profits. This model is predicated on the definition of investment as accumulation of constant and variable capital. 

For Marx, investment is made up of increments in constant and variable capital. In money terms,... 

Taking investment to be made up of new constant and variable capital3 we can write, using (A7.2) and (A7.6),... 

Schmitt (1996 123) also argues against the narrow Keynesian specification of the multiplier as a model of impacts between the investment sector and the consumption sector . This is the approach taken by Nell (2004). Following Marx s definition of investment as increments in constant and variable capital, the multiplier in equation (4.23) is exempt from this criticism, locating increments in both sectors. 

Within each of the two classes in Table V, the first two sets of limits ((a), (b), (d), (e)) use the constant and variable weights, respectively, and assume B and A are exactly known (model-1 in Table IV). The remaining limits involve estimated parameters, based on the design x and the equations of Table III. Method (c) utilizes the parameters of Model-1 and constant weight method (f) uses Model-3 and variable y-errors (weight). 

By means of the method described, the solution of the multicomponent sorption kinetics problem, at both constant and variable surface... 

These are the principal symbols for constants and variables, together with the Parts of the text in which they appear, usually described by equation numbers, but sometimes by section where they are discussed in prose. The tables in which values are listed are also given. A few key units are also included. 

Honjo, T., Packman, S., Swan, D., Leder, P. (1976). Quantitation of constant and variable region genes for mouse immunoglobulin X chains. Biochemistry 15, 2780-2785. 

Kindt, T.J., Gris, C., Guenet, J.L., Bonhomme, F., Cazenave, P.-A. (1985). Lambda light chain constant and variable gene complements in wild-derived inbred mouse strains. Eur. J. Immunol. 15,... 

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