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Firstly, a mod function is usually called with positive modulus (note the variable arrayLength in the original question that is being answered here, which is presumably never negative), so the function doesn''t really need to be made to work for negative modulus. (That is why I mention the treatment of negative modulus in a comment on my answer ...
This used to be implementation-defined in older revisions of C++, but now it''s all fully specified: Division truncates, i.e. a / b is the mathematical value with the fractional part discarded. For example, 9 / -5 is the truncation of −1.8, so it''s -1. The remainder operation a % b is defined by the identity you presented. So let''s compute: (a / b) * b is -1 * -5 is 5, so 9 % -5 is 4.
The sign in such cases (i.e when one or both operands are negative) is implementation-defined. The spec says in §5.6/4 (C++03), The spec says in §5.6/4 (C++03), The binary / operator yields the quotient, and the binary % operator yields the remainder from the division of the first expression by the second.
The storage modulus is related to elastic deformation of the material, whereas the loss modulus represents the energy dissipated by internal structural rearrangements. ... As the number of ...
Is there a modulus (not remainder!) function / operation in Rust? As far as I can tell, there is no modular arithmetic function.. This also happens in C, where it is common to use the workaround you mentioned: ((a % b) + b) % b. In C, C++, D, C#, F# and Java, % is in fact the remainder. In Perl, Python or Ruby, % is the modulus. Language developers don''t always go …
While the loss modulus was not impacted by the different composition of the hydrogels, the elastic storage modulus was increased by the incorporation of CNC, giving the GA-HA-CNC hydrogels the best viscoelastic properties; thus, they are more likely to be applied as wound dressing material than the other hydrogels tested . Finally, Quah et al ...
G''=G*cos(δ) - this is the "storage" or "elastic" modulus; G''''=G*sin(δ) - this is the "loss" or "plastic" modulus ... Deborah, who said "The mountains flowed before the Lord" and who has thus been honoured with the Deborah Number: D e =τ/t. D e is the ratio of the relaxation time τ of the system (say a mountain) and the timescale, t (say ...
Its behavior when dealing with negative numbers or decimals is more complicated. However, understanding how the formula works is important for math lessons and exams. Modulus Of Complex Numbers. The modulus of a complex number can be found using a specific formula.
The ''sum'' of loss and storage modulus is the so-called complex modulus G*. The complex viscosity h* is a most usual parameter and can be calculated directly from the complex modulus. This viscosity can be related to the viscosity measured in a steady shear test by a relation known as the Cox-Merz rule.
In mathematics, we choose inward jumps, i.e. forward direction for a positive number and backward direction for negative numbers. But in Python, we have a forward direction for all positive modulo operations. Hence, your confusion - >>> -5 % 4 3 >>> 5 % 4 1 Here is the python code for inward jump type modulo in python:
If that is the case, then I have seen materials with a Young''s modulus of 120 MPa, but a Storage modulus of 900 MPa. This would make the ball relatively stretchy, but somewhat rigid since it has a ...
In C89/90, either result was allowed. The results you got from division and remainder were required to "fit" together so that (a/b)*b + a%b == a.. Starting with C99, integer division with a negative input is required to truncate toward zero.
As I understand it, the modulus of a positive number x with a number n is - the remainder of x divided by n. But how is the modulus of a negative number calculated? Example - -3 mod 12 = 1, -1 % 19 = 18. I spent more than an hour going through the answers to this question on Math.StackExchange, but nothing made sense to me.
However, it is perfectly fine to write both 18 ≡ 3 (mod 5) 18 ≡ 3 (mod 5) and 18 ≡ −2 (mod 5) 18 ≡ − 2 (mod 5) as 3 ≡ −2 (mod 5) 3 ≡ − 2 (mod 5). As a general statement, we write a ≡ b (mod …
The averaged storage modulus of Type 1 gel (1.9 MPa) is less than the 1 Hz Type 3.1 storage modulus (3.8 MPa) but greater than the 100 Hz Type 3.2 storage modulus (1.1 MPa). In addition, the loss moduli for Type 1 (0.45 MPa) also showed differences compared to Type 3.1 and 3.2, i.e., 0.98 MPa and 0.65 MPa, respectively.
The slope of the loading curve, analogous to Young''s modulus in a tensile testing experiment, is called the storage modulus, E''. The storage modulus is a measure of how much energy must be put into the sample in order to distort it. The difference between the loading and unloading curves is called the loss modulus, E". It measures energy lost ...
You can add some multiple of 5 to the negative number first, to convert it to a positive number with the same value mod 5. You can do that by taking the absolute of the negative number, adding whatever is needed to round it up to the next multiple of 5, and then add it to your negative number, and that should already be a number between 0 and 4.
$begingroup$ @weno You could avoid the reflection formulas temporarily by looking at the $tan(operatorname{arg}(x + iy)) = y/x$ formula, remembering not just to take $arctan$ of both sides, but also to check which quadrant the complex number lies in. This will be a little messy though, and remember, the only possible arguments are of the form $(2k + 1)pi …
"that is the way the Java modulus operator works" Except Java doesn''t have a modulus operator, only a remainder operator. --- Reference 1: Java Language Specification, section 15.17.3. Remainder Operator % .
For example, if I compute 18 mod 5 18 mod 5, the result will be 3 3. This will be because of 5 ⋅ 3 + 3 = 18 5 ⋅ 3 + 3 = 18, but can I have 5 ⋅ 4 − 2 = 18 5 ⋅ 4 − 2 = 18 which gives me −2 − 2? That is perfectly okay because they are in the same equivalency class.
I would be careful. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the …
Some energy was therefore lost. The slope of the loading curve, analogous to Young''s modulus in a tensile testing experiment, is called the storage modulus, E ''. The storage modulus is a measure of how much energy must be put into the sample in order to distort it.
This makes it very easy for all natural numbers. For negative numbers, some conventions want the remainder to be in the interval [-(m-1)..0], some stick with above definition, and some take the solution where |b| is minimal. Thus, you have to try the implementation the compiler or library developer chose.
In mathematics, the modulus must be >1 and the convention is that the modulo operation yields the smallest non-negative integer solution to a+km=b:-7 mod 2 = 1 7 mod -2 Illegal -7 mod -2 Illegal It is easy to extend the definition to include negative numbers (and 1 and -1):-7 mod 2 = 1 7 mod -2 = 1 -7 mod -2 = 1 -7 mod 3 = 2
To answer the question in your title, the modulus (in your example, it is five) must always be at least 2 2 for anything (interesting) to make sense. However, it is perfectly fine to write both 18 ≡ 3 (mod 5) 18 ≡ 3 (mod 5) and 18 ≡ −2 (mod 5) 18 ≡ − 2 (mod 5) as 3 ≡ −2 (mod 5) 3 ≡ − 2 (mod 5).
If it is higher than the loss modulus the material can be regarded as mainly elastic, i.e. the phase shift is below 45°. The loss modulus represents the viscous part or the amount of energy dissipated in the sample. The ''sum'' of loss and storage modulus is the so-called complex modulus G*.
Materials with a large storage modulus are generally regarded as elastic, Poisson''''s ratio can exceed 0.5. It can also be negative, meaning that extension of the material in one direction leads to extension in other directions. ... Modulus of Negative Numbers. Problem: What is -7 mod 5? Solution: To find -7 mod 5, we firstly find the largest ...
What it doesn''t seem to tell us is how "elastic" or "plastic" the sample is. This can be done by splitting G* (the "complex" modulus) into two components, plus a useful third value: …
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