(Music) Pertaining to a style of ragtime piano music having a melody embellished with chords and syncopated rhythms, accompanied by a bass in strict two-four or four-four time. It is often played on an upright piano having its strings muffled to produce a tinny sound; as, a honky-tonk piano. RHUD
Latest posts made by DebrahCom
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RE: honky-tonk
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RE: hilbert space
In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as function spaces. Formally, a Hilbert space is a vector space equipped with an inner product that defines a distance function for which the space is a complete metric space.
The earliest Hilbert spaces were studied from this point of view in the first decade of the 20th century by David Hilbert, Erhard Schmidt, and Frigyes Riesz. They are indispensable tools in the theories of partial differential equations, quantum mechanics, Fourier analysis (which includes applications to signal processing and heat transfer), and ergodic theory (which forms the mathematical underpinning of thermodynamics). John von Neumann coined the term Hilbert space for the abstract concept that underlies many of these diverse applications. The success of Hilbert space methods ushered in a very fruitful era for functional analysis. Apart from the classical Euclidean vector spaces, examples of Hilbert spaces include spaces of square-integrable functions, spaces of sequences, Sobolev spaces consisting of generalized functions, and Hardy spaces of holomorphic functions.
Geometric intuition plays an important role in many aspects of Hilbert space theory. Exact analogs of the Pythagorean theorem and parallelogram law hold in a Hilbert space. At a deeper level, perpendicular projection onto a linear subspace or a subspace (the analog of dropping the altitude of a triangle) plays a significant role in optimization problems and other aspects of the theory. An element of a Hilbert space can be uniquely specified by its coordinates with respect to an orthonormal basis, in analogy with Cartesian coordinates in classical geometry. When this basis is countably infinite, it allows identifying the Hilbert space with the space of the infinite sequences that are square-summable. The latter space is often in the older literature referred to as the Hilbert space. -
RE: patched
Mended, usually clumsily by covering a hole with a patch; as, patched jeans.
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RE: gujarat
Gujarat (, Gujarati: [ˈɡudʒəɾɑt] (listen)) is a state along the western coast of India. Its coastline of about 1,600 km (990 mi) is the longest in the country, most of which lies on the Kathiawar peninsula. Gujarat is the fifth-largest Indian state by area, covering some 196,024 km2 (75,685 sq mi); and the ninth-most populous state, with a population of 60.4 million. It is bordered by Rajasthan to the northeast, Dadra and Nagar Haveli and Daman and Diu to the south, Maharashtra to the southeast, Madhya Pradesh to the east, and the Arabian Sea and the Pakistani province of Sindh to the west. Gujarats capital city is Gandhinagar, while its largest city is Ahmedabad. The Gujaratis are indigenous to the state and their language, Gujarati, is the states official language.
The state encompasses 23 sites of the ancient Indus Valley civilisation (more than any other state). The most important sites are Lothal (the worlds first dry dock), Dholavira (the fifth largest site), and Gola Dhoro (where 5 uncommon seals were found). Lothal is believed to have been one of the worlds first seaports. Gujarats coastal cities, chiefly Bharuch and Khambhat, served as ports and trading centres in the Maurya and Gupta empires, and during the succession of royal Saka dynasties in the Western Satraps era.
Along with Bihar, Mizoram and Nagaland, Gujarat is one of four Indian states to prohibit the sale of alcohol. The Gir Forest National Park in Gujarat is home to the only wild population of the Asiatic lion in the world.The economy of Gujarat is the fourth-largest in India, with a gross state domestic product (GSDP) of ₹16.55 trillion (US billion) and has the countrys 10th-highest GSDP per capita of ₹215,000 (US,700). Gujarat ranks 21st among Indian states and union territories in human development index. Gujarat is regarded as one of the most industrialised states and has a low unemployment rate,
but the state ranks poorly on some social indicators and is at times affected by religious violence. -
RE: map-reader
A map-reader is a person who is skilled in interpreting or reading maps. They can understand and derive meaningful information from various types of maps, including geographical, topographical, digital, road or any other kind of cartographic representation. A map-reader can use this information to plan routes, identify specific landmarks or locations, or analyze spatial data.