kronecker delta sentence in Hindi
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- The " " " or "'multi-index Kronecker delta "'of order is a type tensor that is a completely antisymmetric in its upper indices, and also in its lower indices.
- Here \ gamma _ m is the autocovariance function of X t, \ sigma _ \ varepsilon is the standard deviation of the input noise process, and \ delta _ { m, 0 } is the Kronecker delta function.
- Where \ tau is the stress, \ lambda and \ mu are the Lam?parameters ( with \ mu as the shear modulus ), \ delta _ { ij } is the Kronecker delta, and the strain tensor is defined
- However, when it is understood that no indices will be raised or lowered while retaining the base symbol, covariant indices are sometimes placed below contravariant indices for notational convenience ( e . g . with the generalized Kronecker delta ).
- The commutation relations can be proved as a direct consequence of the canonical commutation relations [ x _ l, p _ m ] = i \ hbar \ delta _ { lm }, where " ? lm " is the Kronecker delta.
- For example, if a Dirac delta impulse occurs exactly at a sampling point and is ideally lowpass-filtered ( with cutoff at the critical frequency ) per the Nyquist Shannon sampling theorem, the resulting discrete-time signal will be a Kronecker delta function.
- Other identities can be formed from the " ? " tensor and " ? " pseudotensor, a notable and very useful identity is one that converts two Levi-Civita symbols adjacently contracted over two indices into an antisymmetrized combination of Kronecker deltas:
- The parameter l is the characteristic length-scale of the process ( practically, " how close " two points x and x'have to be to influence each other significantly ), ? is the Kronecker delta and ? the standard deviation of the noise fluctuations.
- A property that is often useful in probability is that the Fourier transform of the uniform distribution is simply \ delta _ { a, 0 }, \, where 0 is the group identity and \ delta _ { i, j } \, is the Kronecker delta.
- Where m = 0, \ ldots, p, yielding p + 1 equations . \ gamma _ m is the autocovariance function of X, \ sigma _ \ varepsilon is the standard deviation of the input noise process, and \ delta _ m is the Kronecker delta function.
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