Zelen's design, or Zelen's randomised design, refers to a statistical design used primarily in clinical trials to evaluate the effectiveness of a treatment or intervention. Developed by Marvin Zelen in the 1970s, this design is particularly useful for situations where the outcome of an intervention is not immediately observable, such as in cancer treatments. The key features of Zelen's design include: 1. **Randomization**: Participants are randomly assigned to either the treatment group or the control group.

The Frölicher–Nijenhuis bracket is a mathematical construct that comes from the field of differential geometry and differential algebra. It is a generalization of the Lie bracket, which is typically defined for vector fields. The Frölicher–Nijenhuis bracket allows us to define a bracket operation for arbitrary differential forms and multilinear maps.

Jan Tauc is a notable figure known for his work in the fields of physics and materials science, particularly in the study of semiconductors and related materials. He has contributed to the understanding of optical and electrical properties of various materials.

Gromov's inequality is a significant result in the field of differential geometry, particularly concerning the characteristics of complex projective spaces. It provides a lower bound for the volume of a k-dimensional holomorphic submanifold in a complex projective space in relation to the degree of the submanifold and the dimension of the projective space.

A Hermitian Yang–Mills connection is a mathematical concept that arises in the field of differential geometry and gauge theory, particularly in the study of Yang–Mills theories and the geometry of complex manifolds. It is an important tool in areas such as algebraic geometry, gauge theory, and mathematical physics. ### Key Components: 1. **Hermitian Manifolds**: A Hermitian manifold is a complex manifold equipped with a Hermitian metric.

Noncommutative geometry is a branch of mathematics that generalizes geometric concepts to settings where the usual notion of points, coordinates, and commutativity does not apply. In traditional geometry, the coordinates of spaces are commutative—meaning the order of multiplication does not affect the result. However, in noncommutative geometry, the coordinates do not necessarily commute, which leads to a richer and more complex structure.

A nonholonomic system refers to a type of dynamical system that is subject to constraints which are not integrable, meaning that the constraints cannot be expressed purely in terms of the coordinates and time. These constraints typically involve the velocities of the system, leading to a situation where the motion cannot be fully described by a potential function alone.

In mathematics, particularly in the field of topology, a "ribbon" can refer to specific structures that have properties resembling those of ribbons in the physical world—long, narrow, flexible strips. The most notable mathematical concept related to ribbons is the "ribbon surface." A ribbon surface is often used in the context of knot theory and can be seen as a way to study the embedding of circles in three-dimensional space.

Cobordism is a concept from the field of topology, particularly in algebraic topology, that studies the relationships between manifolds. In simple terms, cobordism provides a way to classify manifolds based on their boundaries and their relationships to each other.

In the context of mathematics, particularly in algebraic geometry and algebraic topology, the term "inverse bundle" is not widely recognized as a standard term. However, it could potentially refer to a few concepts depending on the context. 1. **Vector Bundles and Duals**: In the theory of vector bundles, one often talks about the dual bundle (or dual vector bundle) associated with a given vector bundle.

The unit tangent bundle is a fundamental concept in differential geometry and is used in the study of manifolds, particularly in the context of differential geometry and geodesic flows. Given a smooth manifold \( M \), the unit tangent bundle, denoted as \( U(TM) \), consists of all unit tangent vectors at every point in \( M \).

In mathematics, particularly in the context of combinatorial optimization and graph theory, "plumbing" refers to a technique used to connect different mathematical objects or structures in a way that allows for the study of their properties as a whole. It is often applied in the context of manifolds and topology, where complex shapes can be constructed from simpler pieces by "plumbing" them together.

As of my last knowledge update in October 2023, there are no widely recognized works or significant figures specifically known as "Discoveries by Juan Lacruz." It’s possible that this could refer to a lesser-known work, project, or emerging author that has gained attention after my last update.

Wide-angle X-ray scattering (WAXS) is a technique used in material science and structural biology to investigate the atomic and molecular structure of materials. It involves the scattering of X-rays from a sample, providing information about the arrangement of atoms within that sample. ### Key Components of WAXS: 1. **X-Ray Source**: WAXS uses X-ray beams generated from synchrotrons or X-ray tubes to probe the sample.

An anticausal system is a type of system in which the output at any given time depends on future inputs rather than past inputs. In other words, for an anticausal system, the output \( y(t) \) at time \( t \) relies on values of the input \( x(t) \) for times \( t' > t \).

Bin-centres refer to the central points of data bins, which are used in histograms and frequency distributions to represent grouped data. In a histogram, data is divided into intervals (or "bins"), and each bin contains a range of values. The bin-centre is the midpoint of that range, calculated by taking the average of the lower and upper boundaries of the bin.

Delay equalization refers to a process used in various fields, such as telecommunications, audio engineering, and signal processing, to compensate for time delays that occur in signals. The goal is to achieve synchronization or alignment of signals that have been affected by different propagation times or processing latencies. ### Key Concepts: 1. **Purpose**: The main objective of delay equalization is to ensure that multiple signals, whether from different sources or pathways, arrive at a receiver at the same time.

Delta-sigma modulation (DSM) is a technique used in analog-to-digital and digital-to-analog conversion that achieves high precision and resolution. It's particularly useful in applications such as digital audio, sensor signal processing, and any scenario where high-performance conversion is required. **Key Concepts of Delta-Sigma Modulation:** 1. **Oversampling**: Delta-sigma modulation operates by oversampling the input signal.

Delta modulation (DM) is a modulation scheme used to convert analog signals into digital form. It is a simple form of differential pulse-code modulation (DPCM), where only the difference between the current sample and the previous sample is encoded, rather than transmitting the actual signal values. ### Key Features of Delta Modulation: 1. **Differential Encoding**: Delta modulation encodes the difference between successive samples rather than the absolute value of the samples themselves.

The Least Mean Squares (LMS) filter is an adaptive filter used primarily in signal processing and control systems to minimize the mean squared error between a desired signal and the actual output of the filter. The LMS filter is commonly employed in applications such as noise cancellation, echo cancellation, and system identification. ### Key Characteristics of LMS Filter: 1. **Adaptive Filtering**: The LMS algorithm adapts the filter coefficients based on the incoming signal and the errors in the output.