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The dull light gives gentle and even illumination of the ground leading up to the teahouse. Between April and November, only the roofline and treetop can be seen from this angle of view. Under the thin layer of ice on the pond the fish both young and old slumber.
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Un jardin discrètement lové au coeur de l'animation parisienne, proche de Bercy et de la Gare de Lyon.
Espaces dédiés au bien-être, cocons de calme épicés de douceur...
Souhaits de simplicité, de beauté, de sensualité...
Entrez en désir, vos désirs sont des ordres.
A garden discreetly hidden in the heart of the Parisian animation, close to Bercy and to the Gare de Lyon.
Spaces dedicated to the well-being, cocoons of peace spiced with sweetness...
Wishes of simplicity, beauty, sensuality...
Enter in desire, your desires are orders.
Embarking on the intricate journey of mastering Discrete Mathematics, students often encounter challenging assignments that demand a profound understanding of mathematical structures. Discrete Math, with its focus on discreet, countable elements, forms the backbone of various computer science and mathematical disciplines. In this blog, we delve into the complexities of Discrete Mathematics Assignments, exploring their multifaceted nature and offering invaluable insights to conquer these academic challenges. Navigating the realm of Discrete Math Assignment Help at www.mathsassignmenthelp.com/discrete-math-assignment-help/, we aim to provide clarity and guidance, empowering students to excel in their studies.
Question:
Consider a directed graph ( G = (V, E) ) where ( V ) is the set of vertices and ( E ) is the set of directed edges. Let ( n = |V| ) be the number of vertices in the graph. For each vertex ( v \in V ), there is an associated positive integer ( d(v) ) representing the outdegree of the vertex, i.e., the number of outgoing edges from ( v ).
Prove that the sum of the outdegrees of all vertices in the graph is equal to the total number of edges in the graph.
Let ( A ) be the adjacency matrix of the graph, where ( A[i][j] = 1 ) if there is a directed edge from vertex ( i ) to vertex ( j ), and ( A[i][j] = 0 ) otherwise. Define a new matrix ( B ) as follows: ( B[i][j] = d(i) \times A[i][j] ), where ( d(i) ) is the outdegree of vertex ( i ). Show that the sum of all entries in matrix ( B ) is equal to the total number of edges in the graph.
Consider a path in the graph, which is a sequence of distinct vertices ( v_1, v_2, \ldots, v_k ) such that there is a directed edge from ( v_i ) to ( v_{i+1} ) for ( 1 \leq i < k ). Prove that the sum of the outdegrees of the vertices along this path is equal to the total number of edges in the path.
Let ( G' ) be the transpose of the original graph ( G ). That is, ( G' = (V, E') ) where ( E' ) consists of all the edges in ( G ) with their directions reversed. Show that the sum of the indegrees of all vertices in ( G' ) is equal to the total number of edges in the graph ( G ).
Solution:
1. Proof of Outdegrees Sum:
Let ( d(v) ) be the outdegree of vertex ( v ). The sum of the outdegrees is given by:
[ \sum_{v \in V} d(v) ]
Consider each edge in the graph, it contributes 1 to the outdegree of its starting vertex. Therefore, the sum of outdegrees is precisely the total number of edges in the graph.
[ \sum_{v \in V} d(v) = \text{Number of Edges in } G ]
2. Matrix ( B ) Sum:
The sum of all entries in matrix ( B ) is given by:
[ \sum_{i \in V} \sum_{j \in V} d(i) \times A[i][j] ]
Consider each term in the double sum. If ( A[i][j] = 1 ), then ( d(i) ) contributes to the sum. This is precisely the outdegree of vertex ( i ). Thus, the double sum counts the sum of outdegrees, which by part 1, is equal to the total number of edges in the graph.
[ \sum_{i \in V} \sum_{j \in V} d(i) \times A[i][j] = \text{Number of Edges in } G ]
3. Sum of Outdegrees on a Path:
Consider a path ( P: v_1, v_2, \ldots, v_k ). The sum of outdegrees along this path is:
[ \sum_{i=1}^{k-1} d(v_i) ]
Each term in the sum represents the outdegree of the respective vertex on the path. Again, by part 1, this sum is equal to the total number of edges in the path.
[ \sum_{i=1}^{k-1} d(v_i) = \text{Number of Edges in } P ]
4. Transpose Graph Indegrees Sum:
Let ( G' ) be the transpose of ( G ). The sum of indegrees in ( G' ) is given by:
[ \sum_{v \in V} \text{indegree}_{G'}(v) ]
Consider an edge in ( G ) from ( u ) to ( v ). This edge becomes an edge from ( v ) to ( u ) in ( G' ), contributing to the indegree of ( v ). Thus, the sum of indegrees in ( G' ) is equal to the total number of edges in ( G ).
[ \sum_{v \in V} \text{indegree}_{G'}(v) = \text{Number of Edges in } G ]
Conclusion:
In the realm of academic pursuits, conquering Discrete Mathematics assignments becomes a pivotal milestone. With the insights shared in this blog, complemented by the resources available for Discrete Math Assignment Help, students are equipped to navigate the intricacies of this field with confidence. As you embark on your journey through Discrete Mathematics, may this blog serve as a beacon, illuminating the path to academic success. Embrace the challenges, seek assistance when needed, and let the world of Discrete Mathematics unfold as a captivating puzzle waiting to be solved.
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Today we are in Napier one of the cities with the best collection of Art Deco buildings in the world.
An expansive multidisciplinary collaboration between mathematicians, dancers, media artists, composers, and engineers, this complex experimental augmented reality performance is truly the first of its kind. This newest dance performance probes the circuitry connecting the corporeal to the cognitive, questioning the very essence of humanity and machine. Alan Turing is often called the father of modern computing. He was a brilliant mathematician and logician. He developed the idea of the modern computer and artificial intelligence Turing thus gave birth to one physical incarnation of mathematics. His creations are the embodiment of the act of performing mathematics. Although his contemporaries would see a sharp delineation between human and machine, in his eyes, his progeny did not constitute a distant “other”. Rather, he was the father of a “living machine.” How might mathematics manifest itself as physical expression? What binds human cognition and philosophy to a human being’s body? How might this connection dissolve or transform in time? The full-length show follows the emergence of mathematics in relationship to the human body, exploring perception and our physical modes of expression through a complex set of emerging technologies.
Event Link:
grayarea.org/event/discretefigures-rhizomatiks-research-e...
Informacja prasowa
Zduńska Wola, 8 maja 2015
Gatta poleca kolejną nowość: rajstopy bezszwowe Discrete
Przyszła wiosna, a wraz z nią moda na krótkie spódnice i dopasowane sukienki. Wiele kobiet coraz częściej sięga więc po rajstopy. Niektóre wybierają cienkie, neutralne kolory, inne klasyczną cze...
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From a discrete distant, I have been documenting this eagle's nest building and rearing of its' young. Last week shots were heard by the property owner in the area of the nest (it is Turkey season in Ontario). Note the neat round hole in the eagle's tail
An expansive multidisciplinary collaboration between mathematicians, dancers, media artists, composers, and engineers, this complex experimental augmented reality performance is truly the first of its kind. This newest dance performance probes the circuitry connecting the corporeal to the cognitive, questioning the very essence of humanity and machine. Alan Turing is often called the father of modern computing. He was a brilliant mathematician and logician. He developed the idea of the modern computer and artificial intelligence Turing thus gave birth to one physical incarnation of mathematics. His creations are the embodiment of the act of performing mathematics. Although his contemporaries would see a sharp delineation between human and machine, in his eyes, his progeny did not constitute a distant “other”. Rather, he was the father of a “living machine.” How might mathematics manifest itself as physical expression? What binds human cognition and philosophy to a human being’s body? How might this connection dissolve or transform in time? The full-length show follows the emergence of mathematics in relationship to the human body, exploring perception and our physical modes of expression through a complex set of emerging technologies.
Event Link:
grayarea.org/event/discretefigures-rhizomatiks-research-e...
An expansive multidisciplinary collaboration between mathematicians, dancers, media artists, composers, and engineers, this complex experimental augmented reality performance is truly the first of its kind. This newest dance performance probes the circuitry connecting the corporeal to the cognitive, questioning the very essence of humanity and machine. Alan Turing is often called the father of modern computing. He was a brilliant mathematician and logician. He developed the idea of the modern computer and artificial intelligence Turing thus gave birth to one physical incarnation of mathematics. His creations are the embodiment of the act of performing mathematics. Although his contemporaries would see a sharp delineation between human and machine, in his eyes, his progeny did not constitute a distant “other”. Rather, he was the father of a “living machine.” How might mathematics manifest itself as physical expression? What binds human cognition and philosophy to a human being’s body? How might this connection dissolve or transform in time? The full-length show follows the emergence of mathematics in relationship to the human body, exploring perception and our physical modes of expression through a complex set of emerging technologies.
Event Link:
grayarea.org/event/discretefigures-rhizomatiks-research-e...
An ingenious way of conducting guided tours by a Korean tour group. The entire group were given wireless earphones that receives transmissions from their tour guide. The tour guide then speaks into a microphone and his voice transmitted to his group via the wireless earphones. This allows the tour guide to speak discretely without having to raise his voice for the entire group to hear.
Taken at the inner temple area of Angkor Wat.
Mouse-over photo to see notes.
An expansive multidisciplinary collaboration between mathematicians, dancers, media artists, composers, and engineers, this complex experimental augmented reality performance is truly the first of its kind. This newest dance performance probes the circuitry connecting the corporeal to the cognitive, questioning the very essence of humanity and machine. Alan Turing is often called the father of modern computing. He was a brilliant mathematician and logician. He developed the idea of the modern computer and artificial intelligence Turing thus gave birth to one physical incarnation of mathematics. His creations are the embodiment of the act of performing mathematics. Although his contemporaries would see a sharp delineation between human and machine, in his eyes, his progeny did not constitute a distant “other”. Rather, he was the father of a “living machine.” How might mathematics manifest itself as physical expression? What binds human cognition and philosophy to a human being’s body? How might this connection dissolve or transform in time? The full-length show follows the emergence of mathematics in relationship to the human body, exploring perception and our physical modes of expression through a complex set of emerging technologies.
Event Link:
grayarea.org/event/discretefigures-rhizomatiks-research-e...
Team:
The idea is to have a few discrete construction systems that do not have many variations to save on cost. The combination of them provides the variation instead.
The orange panels are 4x10 and can be finply or a variety of other inexpensive materials. The planter and its armature are the dark rust color stripes. The window sills are either at finish floor or at 30", up to the 8' ceiling. The walls can be built panelized or modular if desired. To adjust solar gain and views, there are sliding wood screens which provide optional placement. Their track is resting on the planter armature. They can even slide out onto the deck.
At the finish floor you will see a series of small screened awning windows below the planter. These windows bring cool air into the rooms and vent out into the hallway, which is next to the tower opening.
very thick platy structure
Soil Peds are aggregates of soil particles form as a result of pedogenic processes; this natural organization of particles forms discrete units separated by pores or voids. The term is generally used for macroscopic (visible; i.e., greater than 1 mm in size) structural units when observing soils in the field. Soil peds should be described when the soil is dry or slightly moist, as they can be difficult to distinguish when wet.
Platy soil structure is characterized by peds that are flat and platelike. They are generally oriented horizontally. A special form, lenticular platy structure, is recognized for plates that are thickest in the middle and thin toward the edges. Platy structure is usually found in subsurface soils that have been subject to leaching or compaction by animals or machinery. The plates can be separated with little effort by prying the horizontal layers with a pen knife. Platy structure tends to impede the downward movement of water and plant roots through the soil.
There are five major classes of macrostructure seen in soils: platy, prismatic, columnar, granular, and blocky. There are also structureless conditions. Some soils have simple structure, each unit being an entity without component smaller units. Others have compound structure, in which large units are composed of smaller units separated by persistent planes of weakness.
For more information about describing and sampling soils, visit:
www.nrcs.usda.gov/resources/guides-and-instructions/field...
or Chapter 3 of the Soil Survey manual:
www.nrcs.usda.gov/sites/default/files/2022-09/The-Soil-Su...
For additional information on "How to Use the Field Book for Describing and Sampling Soils" (video reference), visit: