Many mathematical properties possessed by functions of several variables are couched in geometric terms and with reference to elementary set theory. In this introductory chapter I will revisit some of the concepts that will be needed in later chapters. For example, vector calculus springs naturally ...
Ushiroya, N.: Mean-value theorems for multiplicative arithmetic functions of several variables. Integers 12, 989–1002 (2012) Article MathSciNet MATH Google Scholar Vaidyanathaswamy, R.: The theory of multiplicative arithmetic functions. Trans. Am. Math. Soc. 33, 579–662 (1931) Article Math...
Remotely-sensed data on terrestrial characteristics and variables such as tempera- ture, rainfall, humidity, along with other environmental factors, govern the distribution of infectious agents as well as the intermediate hosts and vectors they might utilize. Therefore, the application of this new ...
You can create an S-function that is reentrant by using DWork vectors that the engine manages for each particular instance of the S-function. DWork vectors have several advantages: Provide instance-specific storage for block variables Support floating-point, integer, pointer, and general data types...
For both matrices and arrays, the dim function returns a vector of integers of the dimensions of the variable: dim(three_d_array) ## [1] 4 3 2 dim(a_matrix) ## [1] 4 3 For matrices, the functions nrow and ncol return the number of rows and columns, respectively: nrow(a_matrix...
Apply functions to a vector over()applies one or several functions to a vector. We can use it insidedplyr::mutate()to create several similar variables that we derive from an existing column. This is helpful in cases where we want to create a batch of similar variables with only slightly ...
Amebiasis represents a significant global health concern. This is especially evident in developing countries, where infections are more common. The primary diagnostic method in laboratories involves the microscopy of stool samples. However, this approach
Using Functions − MATLAB functions like linspace, ones, zeros, and rand can generate vectors with specific characteristics (e.g., a range of values, all ones, all zeros, random values).Vectors in MATLAB allow for various operations such as addition, subtraction, element-wise multiplication, ...
The definition of divided and finite differences can be used in the definition for convex functions of several variables. This type of definition was firstly introduced by Popoviciu in [57]. Theorem 2.8 Let f : I1 ×I2 → R be (2, 2)−convex such that fxx(x0, y0) ≥ 0, fyy(x...
We consider 3-point and 4-point correlation functions in a conformal field theory with a W-algebra symmetry. Whereas in a theory with only Virasoro symmetry the three-point functions of descendant fields are uniquely determined by the three-point function of the corresponding primary fields this ...